Honda 1985 200m won't start?

I have a old honday 200m three wheeler and the pull starter cam off. Easy fix, just buy a new battery and pop it in. The battery worked for about a week or so, and when I wnt to start my three wheeler, the green nuetral light wouldn't come on soh I couldn't start it. Charged the battery, and it worked. A couple of times i'd be out riding and turn it off to stop and look at something and this would happen. I would have to roll it home.. it would also happen when I would drive up to my house, go inside for maybe 20 minutes and come out & try to start it and it wouldn't work.could it be over heating? It wasn't on a hot day I don't think. Maybe 85 degreese ferhenite. Please help, as this isgetting very annoying, and I don't feel safe riding anymore. The manual also dosnt help very much. That's to all the help in advance!