OBK
Sounds like you are heading for a new battery!
Get one now; it is pretty inevitable that you need one and it saves you a lot off hassle and irritation.
FWIW
I always pull the prop through for as many blades as there are cylinders.
Of course make sure mags off; throttle closed and brakes on.
Serves 2 purposes:
1. You check the compressions and ensure they are all similar.
2. Breakes the oil film and is said to reduce the resistance when starting
Make sure you are priming adequately (which can be quite a bit more if it gets cold)
Dunno where you are based but here in middle England it has not been really cold yet so if the same applies to you I would expect not too many starting problems just yet.
So if you do think about a new battery and if that does not sort the problem (although I suspect that it will be fine then if you can handswing it and get it to go on the third attempt) get an engineer to have a closer look.
Starting probs in an engine which was fine until recently may well indicate more problems on the way!
MHO of course
FD