intermitten starting

About 6 months ago my girlfriends 95 Grand am decided not to start every now and then. It would start with a jump, go fine for a few days then not start again. Hot or cold never made a difference. I never did anything to it and it's been going fine since. 6 months later, it's starting to do it again. Today it's fine. Tomorrow it won't start. Just clicks. After a jump, It goes fine. For the next week, it goes great. I've checked the battery connections, and alternator. The green light shows good in the battery, but could it still be bad? (and when it cranks, it goes good) If it's a bad connection, Why would a jump get it going?
Very Confused

how old is the battery? did not see one with the eye for a long time.