A bit late to this party but the information might be useful for others: I've been using rechargeable NiMH batteries in my 2018-issue Audiomoths for a couple of years now with no problems whatsoever. I record 24 hours/day (3600 second duration, 0 second sleep, 32kHz, gain = Med) and get about 190 hours every time (about 8 days). My worst ever was still in excess of 7 days.
The batteries are Ikea LADDA 2450mAh (according to internet rumour these are re-badged Eneloop Pro batteries - that might or might not be true but they do perform very well for the price!) With predicted daily energy consumption of 300mAh this suggests that the batteries are almost completely drained before the unit stops working. In fact some are so well drained they need to be jump-started before they can be recharged.
While the nominal voltage on these is 1.2V, when fully charged they actually hit about 1.32-1.35V. Thus the concern that 3xNiMH batteries are already very close to the 3.3V operating minimum might not apply to all NiMH batteries (for what it's worth the Audiomoth configuration window rates my starting voltage as 4.1 or 4.2V)
That said, a few notes of caution:
1. There are a lot of very cheap/ bad/ fake NiMH batteries on the market. I can vouch for the LADDA 2450s and (genuine) Eneloop Pros but haven't tried anything lower spec.
2. I'm using my Audiomoths in a temperate environment (typical temperature range is approx 5-35 degrees Celsius, and never less than zero) - I have no idea how well NiMHs work in more extreme temperatures.
3. I've only recorded birdsong until now (32kHz). I am running some tests at 384kHz and will report how the NiMHs hold up against the predicted daily usage.
