The battery management system in N810 is also unable to safely charge very degraded (50 - 60% of original capacity remaining) batteries when supplied by the strong charger included with N810. A weaker charger would perhaps be able to charge a degraded battery, but the power consumption from rebooting would draw more power than is being put in, so it'd probably never reach net positive charge rate.

tl;dr: Yes, try a new battery