The battery is good, but sometimes it won't.

The battery is good, but sometimes it won't start, the relay is clicking but won't go through to the starter solenoid. One thing I do to solve is to unplug the solenoid for 15 minutes then reconnect afterwards so it'll start. This isn't a permanent solution. What is the probable cause for this problem?

I also noticed that when the car is parked for a few days, the battery gets drained. When I disconnected the solenoid connection for a month the battery is still good. I'm assuming that the first problem is related to this one as well.