Not ruling out the battery wasn't checked properly, but it sounds, to me anyway, that the system is not charging.
Don't forget it's hard to diagnose something without actually being there, not doubting anything you say but there could be something that would slap a person in the face should you be in front of it and have seen it before.
The times you describe as far as starting, running, starting again etc. sound as if the bike is running of the battery and the battery only.
There is a good troubleshooting chart whose location I can't remember, that'll lead ou thru a sequence of test for the charging system. Someone will post it I'm sure shortly
In a nutshell you check for 70-90VAC directly from the stator when running around 3000rpm. Should be 3 yellow wire and you check between any two. Note that it's AC not DC you're looking for.
If that checks out you then check the DC voltage at the battery, approximately 14-14.5VDC.
Wait till someone posts the site for the chart, do your checks and post back. If you're not sure post back and ask questions.....Mike