It shouldn't be a problem as most modern electronic devices contain a small backup battery designed to provide enough power to retain your settings in case the rechargeable battery goes dead.

I haven't timed how many hours my Libre gets on a full charge yet. I need to do that, but I keep forgetting to write down the time spent reading. On the other hand, if it lasts 8-10 hours that is the most I would normally read in a day, so I could recharge it every night if I needed to. When travelling I'm always near a computer or AC wall outlet. It definitely doesn't have the longevity of my Sony PRS300 e-Ink reader, but then again the e-Ink readers don't display text as clearly as the Libre's greyscale, reflective LCD. so far I've been averaging 3 to 4 days while reading 4 to 6 hours each day before the battery low warning message appears.