I can attest that my Libre allows me to read 4 to 6 hours per day for at least 3 or 4 days before I get the low battery warning. Although I've never actually written down and added up the time, I think it goes at least 12 hours and probably over 20 hours on a charge. As long as you are near a computer with a USB port or an AC wall outlet, you only need as much battery longevity as you can read in a single day because you could charge it every night if necessary. Vacations and travel would be the exception of course.

I would reset the device then charge it all the way up until the charging animation stops animating. Then read until you get the battery low warning message and charge it all the way up again. Repeat this at least 3 times to condition the battery. If this doesn't help then you probably have a bad battery.