Could easily be a factor.
Now for the science bit- pay attention
There are three parts to the stator, each produces current for just under half the crank rotation, so by overlapping all three you get a near- constant flow of current.
The current produced by each sector at other times is -ve, not +ve, so the rectifier part of the reg/rec turns this into heat which is dissipated to the air.
Now all you're left with is a (always +ve but varying in voltage) flow of current that goes into the regulator bit.
That is then regulated to a voltage that can't exceed the voltage that the battery can accept. (about 14.6v or thereabouts).
The battery "buffers" the stored electricity, and delivers it to all of the electrical components on the bike via the wiring harness.
So if one of the stator's outputs isn't contributing properly to the charging system, then you might have as little as 2/3 of the charging current going to the battery, which might then not be sufficiently charged to hold enough stored current to easily start the bike. The other 1/3 is at least partly being used up as a small spark arcing over the gap in your contact, making heat and melting the plastic.
The battery loses a bit of it's stored charge over time, so if it isn't fully charged when you stop the bike there'll be even less when you come to start it again, and if there's not enough.....
BTW, the engine's quite a load to turn over, especially in cold conditions, so I'd advise always turning off all electricals when starting it, including lights and heated grips, external power to sat-navs etc.
Once it fires, turn them back on.
It's not falling off, it's an upgrade opportunity.
). 
