I have been testing an Argon to see how long it can run waking up every hour from deep sleep.
Was working great, had a LiPo battery attached. However, once battery (as reported by the argon) dropped under 3.3v (3.2 ish reported a few times, then stopped waking up. pulled the battery, plugged back in, it woke up, but then after deep sleep it won’t wake again 
I have it plugged in and charging now, will see if it can wake from sleep while charging.
I believe what you described is expected behavior.
A Li-Po @3.2V is discharged…too far.
Data sheet says down to 3v (has safety circuit that will cut off at that point). I’m guessing the Argon has it set to 3.2 or doesn’t have a buck/boost, only LDO voltage converter?
is there a way to set the Low voltage cutoff on the Argon (assuming it has one)?
It’s likely that your Li-Po cant meet the startup current required by the Argon when it’s depleted below 3.3V. There isn’t a setting to change that.
The recommended operating conditions say 3.3V minimum:
The chemical energy available in a Li-Po drops off rapidly at the bottom of it’s voltage curve.
I’d say to terminate your discharge test at ~3.3V and record the results.
Be sure to document the battery size, ambient temperature, firmware version, test code, etc, as these will all impact your results.
Argon Tests would be great info to add on this forum 
ah, thanks @Rftop current draw is likely the case… forgot voltage is only part of the equation 