Why did my triumph spitfire just die?

my 1970 spitfire was running perfect when i got it, it ran for like 2 or 3 hours just fine, then it just died. i replaced the battery today cause the auto place said my old one was shot, after i did that it ran perfect for about 15 min. then died again. i cant figure out why it died and not sure what happened, has anyone else had this problem or does anyone else have any idea on what to look for to fix? thank you.