Why is a common LED failure mode to flicker astably or oscillate?
The problem is not in the LED.  The problem is the LED is misunderstood.

Almost everything associated with an LED is thermal related.

I do not know where you gathered your claims on the various devices but I doubt what you describe is the result of a single phenomena. Nor do the issues manifest in an identical fashion. 

I can assure you it has nothing to do with the LED and everything to do with the LED driver and a design flaw.  

If an LED device does not have a dimming feature it is still likely the LED driver will be dimming the LEDs to regulate the current.

The most likely causes would be over voltage and under voltage protection built in the driver chip or a code error when the LED is controlled by a micro-controller. 

LED present a load  characteristic that is much different than digital devices and other loads that require constant voltage.

Forward voltage characteristic is not just a function of forward current. Looking at the datasheet the prominent I-V curve is shown with voltage as if it is an independent quantity. The designer looks at this curve to get the voltage that matches the desired current to be used. 

The forward voltage is not just current dependent but temperature and varies with the fabrication process from one LED to the next even coming off the manufacturing line one after another. 

When LEDs are strung in series the forward voltages vary unpredictably. It is not unusual for a sting's forward voltage  to vary outside the intended design parameters.  Increasing the number of LEDs in a string will increase the potential difference between Vmin and Vmax.

A constant current source must operate over a wide range of output voltage and maintain the current.  The min max rage is used to select the regulator topology, the IC, and the passive components.  

When designing the regulator with typical values, the input voltage will have it's variance maybe 5%, headroom is designed to be tight, and the output voltage a buck regulator will lose regulation with a small increase in forward voltage.  A buck regulator designed for the typical Vo will be unable to control the current when V out max exceeds minimum input voltage. 

Dynamic resistance is used to select the output capacitance for the desired ripple. In a voltage regulator the load resistance is simply Vo/Io. With LEDs load resistance is replaced with dynamic resistance. Using typical values for Vf and If will lead to incorrect results that are 5 to 10 higher than the true Ro value.  The dynamic resistance is derived from the datasheet's I-V curve. The I-V curve is only  one typical instance.

UPDATE

I have some new information.  First I will address your comments.


  WRT battery-life, buck regulation would appear to be a poor choice for
  a flashlight.


A flashlight is likely to use a buck regulator. Battery voltage rarely will match forward voltage.  A buck regulator is the most efficient, lower cost, less real estate versus a boost driver. A linear regulator would be too inefficient.  


  Isn't the forward voltage of an LED, as with all solid-state diodes,
  determined by the band-gap of the junction materials? How can this
  vary substantially from one device to the next?


Variance in the forward voltage is a characteristic of the manufacturing process. The manufacturers will bin LEDs by forward voltage. 

The following is a quote from LumenHub


  The coating processes (epitaxial growth and phosphors) create
  significant inherent variations that impact the lumens, color
  temperature and voltage of the LEDs. Even with all of the R&amp;D efforts
  underway and the billions of dollars spent within the semiconductor
  industry to minimize this production variation, the end result is a
  process that is not capable of producing highly consistent and tightly
  controlled production of LEDs. So, in an effort to maximize yields
  (and with a knowledge that the lighting industry has a wide range of
  needs), LED manufacturers sort their production into lumen, color and
  sometimes voltage bins.





  You also say, "When LEDs are strung in series the forward voltages
  vary unpredictably." I think you may be confusing series with
  parallel.


When LED are strung in series the individual forward voltages are additive.  I make strips of 16 LEDs and the forward voltage of each strip varies significantly.  One strip may get mostly LEDs that operate below typical while another above typical. 

It is the above typical that is the bigger problem with a poorly designed driver with insufficient overhead.

Forward voltage is a function of manufacturing process, forward current, and temperature.  Each one of these factors has its own intrinsic variations from one LED to another. These variations will alter the I-V curve significantly. Yet an engineer will use the one typical I-V curve with one temperature (25°C),  test current (350mA), and the typical forward voltage for their design parameters. 

The I-V curve in the datasheet is typical and there is nothing typical about an LED. That datasheet I-V curve is in a different ball park than real life. 

Many of the characteristics in the LED datasheet are spec'd at 25°C.  No LED Light Bulb is going to operate at 25°C.     

New  

There is flicker associated with all lighting. This flicker is in the 100-200 Hz range from poorly designed and PWM dimming LED drivers. Although there is some talk about  saccadic eye movement where the eye can see a harmonic frequency of the flicker from PWM regulation. 

Output capacitance and inductance affect the PWM switching and ripple.  Many drivers do not use an inductor and just turn the LED of an on. It is like the blind leading the blind out there.  Somebody comes up with a bad idea, posts it on the Internet, and other follow.  

It is possible you are more susceptible to seeing flicker. There are some neurological factors in the way flicker is perceived. 

The following is an article about flicker, saccadic eye movement, and poor LED designs at the cause. How to design an LED circuit to not have flicker.     

Designing to Mitigate the Effects of Flicker in LED Lighting 

UPDATE II

So you want SUPPORTING EVIDENCE? 

Why did the original post say about 10Hz and later you say 15-18Hz was measured? 

Supporting evidence is not there in the form that flicker is caused by under voltage lock out in the buck converter.  It is much more vague.

Example this article Buck Regulators Make Driving High Brightness LEDs Easy  says "You can overvoltage the switch, you can overvoltage the current-sense pin, and basically have anything from a little bit of LED flicker to a destroyed device."

Example: The best IEEE study on flicker A Review of the Literature on Light Flicker:... could do was citing another study: Rand , D. , Lehman, B. , and Shteynberg, A. (2007) Issues, Models and 30 Solutions for Triac Modulated Phase Dimming of LED Lamps , Proc. IEEE 31 Power Electronics Specialists Conference

The Rand study looks only at the AC/DC rectification stage points to a problem in the DC/DC  with almost nothing said about what actually causes the flicker. On page 1402 they just say "Thus,  simple  buck  derived, low  cost, systems  are  primarily  utilized  after  the  rectifications. There
are  numerous  IC  drivers  with  dimming  capabilities on the
market, yet these systems typically have difficulty with phase 
modulated dimmers."

In the press you will find variations of this: LED Magazine, Understand the lighting flicker frustration and this: LED Journal, Reducing Flicker in LED Lighting

Then there is technical papers that say nothing like this:  Flicker Parameters for Reducing Stroboscopic Effects from Solid-state Lighting Systems 

Even a Cree White paper is just a rehash of the same, you will see the diagrams in this paper in many of the published articles:  Cree, Flicker
 happens. But does it have to?

The bottom line is, as I first said, it is NOT the LED, it is design flaws in the driver. LEDs do not fail very oven in the first 50,000 hours if not abused by heat.  An LED's flux output degrades with use but opens and shorts are very rare.  So rare Lumileds white paper makes a case that their Rebel LED will never fail in the first 80,000 hours.    

The best I can do is recreate it in the lab (which I have done) as I described and video the flicker.   

Of all of the above there is very little talk about flicker in the 10-20hz range. I do not know where you got this "Many have seen..." but that I have to dismiss without supporting evidence.  But I know it is real because I can reproduce it in the lab. I see lots of very bad LED designs and I do see low frequency flicker in the Lab.    

I do not understand those that ask for citations supporting what I say.  I read stuff I remember. I do not catalog the citations of everything I read. I connect the dots. I share that information I have gathered over the past 40 years and all I get is "personal conjecture and guesses and no supporting evidence"   Personal conjecture, some, but not Guesses!  There is nothing I said above that is a guess, it is all based on real facts.

UPDATE III

I have a 15 second video. For the first 10 seconds I am increasing the amps from a Meanwell HLG-60-54B Constant Current supply from 700mA to 1.25A.  

It is driving two parallel strings of 16 Cree XPE Red and Blue LEDs.

Each string is connected to a LM3466 linear current regulator. The regulators ensure the forward current between the two strings remains the same.   

The Red string has a forward voltage just under 30 volts and the blue just over 44 volts.

At about 1A the red triggers the under voltage and 3 seconds later is locked out and remains off. At 700mA the two boards will run all day.

Video is 720p (1280x720) in 2 formats, webm 4MB and mp4 20MB 

LINK to HTML:  15 second MP4 video of flicker HTML5 Video Player webm and mp4
LINK to 10MB mp4 file: 15 second MP4 video of flicker,  mp4
LINK to 4MB webm file:15 second MP4 video of flicker, webm