1995 Ford Probe Battery Always Needs Charging

Approx 1 year ago started having problems with car. Keyless entry remotes stopped working at the same time that the battery needed replaced. After only a few months, we would have to have the car jumped EVERY time we wanted to drive it. The lights wouldn't turn on, no power at all to the car. Eventually found that a light in the glovebox was on constantly so we thought it was draining the battery- took out lightbulb, assumed problem solved. Still had to have car jumped, only drove it occasionally. Had battery and alternator tested, alternator tested fine, battery said that it just needed charged. Eventually replaced battery anyway, and car worked fine to drive on a daily basis. Took keyless entry remotes to dealer, they said that the whole module was bad. Left car sitting for 5 days and now everything is dead again. Is this a sign of an underlying electrical problem?