When NiMHs run down they fall off a cliff. That is, they maintain a steady constant voltage (of approximately 2.4V for a good pair) for 95% of their runtime. Of the other 5%, 3% is when they are fresh off the charger and a bit 'hot', and the remaining 2% is at the end of the runtime when they start to dip below their plateau voltage. It is important to stop draining them at this stage, which is why the Garmin shuts down, but even if it didn't the cells would be sucked dry (and possibly damaged) only a very few minutes later.
So - with the GPS set to 'NiMH' in setup, the warning is presumably triggered around 2.25V and by then the NiMH cells have less than half an hour in them. Suppose, with the same setup, you have a pair of lithiums on board. These run at a higher voltage than the NiMHs (around 2.8V for a pair, assuming no regulation**) but this steadily and gracefully diminishes, and at some point they dip below the NiMH curve and the warning is triggered. However the lithiums still have plenty to give, and could still take hours to drop from 2.25V (warning) to 2.1V (shut down).
** I think there probably is some regulation, because the runtime of lithiums in a Garmin is prodigious - in 2007 and using a Legend Cx with lithiums on board, Sheila rode from Paris to Brest and back to Fougeres before she had to swap them out. These days as a tourist, using an Etrex 30, she gets 5 touring days from a pair of lithiums.
So I carry a spare set and swap them out/recharge after every 2nd riding day.
I can see that has a lot of advantages. But it requires;
- carrying more cells-per-trip than my skinflint strategy. and
You don't carry a spare pair at all? I would at least carry a pair of lithiums and hope never to use them, in the same way that I carry a 2nd spare inner tube. Lithiums weigh next to nothing, and have a 'use by' date somewhere in the next decade. Even if you do have to use them for a few hours, they can go back in the luggage and still be good to go in 5 years time when you need them again.