2003 w/ intermittent starting issues?

So I have combed the threads here and done some investigating but now I need to ask. Just acquired a 2003 abs model w/30,000. Guy I purchased from gave me maintenance records all the way back to new, also included paperwork for the r/r recall having been done. Additionally he had put in brand new battery prior to selling.
I left the keys in ignition in off position overnight and the Fourth time I go to ride it she's dead, but push started just fine. So i stop leaving key in ignition now.Rode for about an hour and battery seemed to hold a charge because when shut off she would start just fine. Ride her for about another week three or four times and then same thing occurs.
So I disconnect negative terminal and use test light to check for a draw and nothing, no light so I guess I'm good?
Hasn't happened again (3 days) but still leaves a thought in the back of my mind.

Any guesses as to what may be happening? Or is it just gremlins in my starter?

 

Ok I will do that today. Thanks

 

The planet gods are jealous on us because we ride VFR's...

 

So my charging system seems to be working. 12.6 v sitting w/ key off. 12.4 v with key in on position. 12.75v when idling. And 13.3v at 5k RPM. So im still not sure why the battery dies occasionally?

 

Everything looks good (like brand new) and I stuck battery on charger overnight. According to electrosport fault finding guide my numbers are good so we will see. If it happens again I might have to get battery load tested again. All connections are tight.