Here's a list as you have to accept that it could be any one or two problems. Yes batteries can show that until current is drawn and rappidly decrease usually through having knackered cells.
1. A knackered battery if it's an old one. Get it tested.
[test also starter solinoid]
2. Alternator fault draining the battery believe called 'open circuit'.
3. Wiring or switch fault other electricals. auto electrician will find the fault if any.
4.I had this one: Starter drawing power from battery but not pushing out power to start the engine giving impression of a flat battery. Work mechanic tested starter and it was faulty he fixed and no problems after that.
Check in sequence.
Bob
December 2010
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