(Micro) USB Timed Relay
You want some form of "Real Time Clock"
Web searching RTC and/or "Real Time Clock" will show you much.  

I'm advised that the RPM has no low power sleep mode.
While you cannot enable an internal micropower Pi RTC mode you WILL be able to have it woken (or turned on) periodically, allowing it to check if it wants to be awake and, if not, again turning itself off completely.  A simple hardware counter and power up circuit could draw under 1 microamp and wake the system hourly or daily or ... . A more intelligent system (as simple as eg an Arduino or an RTC IC) would allow you to set the "delay time to next wakeup". 

You could (with certainty) use an eg Arduino with wake up / alarm capability to restart the Pi. With due care (app notes available) current drain can be half an oily rag (ie under 10 uA with eae and under 1 uA with a little more effort.)
[A 100 mAh LiIon single cell will provide 10 uA for over a year]. 

There are numerous RTC ICs available.
Some will have "alarms" (interrupt drives or switched turn on, or ... for Pi).

Asian suppliers on AliExpress sell many RTC modules with a range of capabilities. Prices start from about $0.00 ish.

You COULD use a classic low power counter and power up and have the Pi check time etc and resleep if desired. The effort and cost would be higher than alternatives.



Ultra low power Arduino:

Here is how to operate an Arduino Pro-Mini (the Pro being an inexplicable but irrelevant label) at about 5 uA in sleep mode but WITH the watchdog timer running.

ARDUINO LOW POWER - HOW TO RUN ATMEGA328P FOR A YEAR ON COIN CELL BATTERY

He makes use of this excellent low-power Arduino library to achieve various low power modes. 

Pro-Minis are available for $2 (or less) from China.

Aliexpress Arduino Real Time Clock - cveat emptor, as ever, but most probably OK.



Various RTC modules from Digikey here
 and here 

RTC 1307 'Hats' / modules ... intended for various systems

here



Olde Technology - CD4060 self oscillating divider:

It's been quote some decades since I've used these - but I think a wakeup oscillator with a current in the 1 - 5 uA region should be possible.

CD4060 - Digikey $US0.53/1.
Needs 2 resistors and a acapacitor to operate.
IC quiescent is 5 uA max, 40 nanoamp typical (! :-) ) at 5V.
Add oscillator current of Vcc/Rtiming - say maybe 1 uA or less, and the oscillatior gate may draw more in the transition region depending on how good a job they did.

See fig 12 for circuit.