Oscillator Driven LED - Not Oscillating
Short:  Short circuit Q1 C-E with metallic shunt on "bad" circuits.
 What happens? 



Review what's known:

The CR2032 is being thrashed to far beyond its usual ratings and its voltage will sag to 2.5V or less.

Q1 on/off circuit seems unnecessary -  The transistor used has a high Vsat and may drop almost a volt at 100 mA. Hard to be sure from datasheet. Measuring Q1-VCE when on may be informative. I only came to that part of the ciruit after going obver the IR part so the following omits the Q1 voltage drop which may be significant. Try bridging Q1 with a metallic short to turn circuit on and see if it helps bad circuits work.

Having Q1 in series with Q2 is unnecessary. Q2 can be arranged to be very hard off with battery across it + LED at all times. Then just switch Vcc to opamp when needed. As opamp current is low you can possibly switch batt5ery directly via SW1 depending on type of switch. LED current then never goes through switch. 



Apart from Q1 Vsat issue: 

LED datasheet here  about 1.5V at 100 mA.

CR2032 typical datasheet here = Vout at 100 mA about 2.5V - maybe less. Not intended for this sort of loading. 

Attempted current = ~~~= (Vbat-VLED)/Rseries = (2.5-1.5)/6.04 =~ 160 mA.
 So battery voltage will sag muchly and LED voltage rise slightly until voltages match.

FCX690 transistor datasheet here is made by Zetex so must be good ! :-).

Base drive is about (Vopamp-Vbe)/Rb = (2.5-0.6)/2200 ~= 0.85 mA.
 Transistor Beta (current gain) is awesome (400 ish at high current albeit with high Vce.) so drive provided is enough to saturate transistor.

Transistor saturation is higher than some - probably about 0.9V at 100-200 mA
 Still not enough to greatly change the above overall current drain estimate.

SO

It's all rather hard on the battery but it SHOULD work with a newish battery. Unknown is length of on time, actual battery voltage under load, ...

Key questions are:


Are all batteries new.
Has battery - LED - ground current path been checked to ensure no high resistance additions by mistake. Eg battery connections, R5 or R7 have some values wrong by factor of 10 or 100 or ... . (Happens)
What is voltage high and low of waveform at op amp output.
What is battery voltage before and during switching attempt and what is battery voltage trace like during switching.
What is on/off duty cycle, how often switched, how long on?

-What is waveform high/low voltages at Q2 base.




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