I still have trouble thinking it's a relay as suggested, and to troubleshoot a relay that only 'sometimes' sticks would seem to be very difficult. If it is a relay, tapping on them (or the starter) sometimes works. Not that it would revive a dead battery.

I personally wouldn't trust that the connections are good, and it is simple enough to clean and attach them again yourself, knowing they are good. Be sure to check the negative ground cable to the frame. And maybe you did.

Let's look closer: When the battery 'goes flat' does that mean no accessories work at all or just weakly? (headlights shine at all? wipers function at all?).

With battery fully charged, disconnect the neg battery cable. Using an ohmmeter, connect a lead to the battery cable and the other to the negative battery terminal. If more than 5 or 10 milliamp draw is noted, remove one fuse at a time, rechecking the draw after each removal, to find the drain.

On some cars the auto trans will prevent the car from starting (my 850 did this once). Releasing the handbrake and moving the car slightly allowed the car to be started. If it's a manual, the clutch switch sometimes fails.

Perhaps these things won't solve the problem. I'm just brainstorming on you.
Good luck.
Don M