Windows XP on thinkpad T41

Looking to purchase a used ThinkPad T41, but discovered a problem. When on battery power with a fully charged battery the system boots up, runs for several minutes on a program that I select, then Freezes briefly, then reboots. Over and over again. When plugged into an A/C outlet the unit works fine! I’m thinking this is a software problem with XP, but I’m not sure where to look.