If the bike runs okay with a fresh battery charge, then it is time scrutinize your charging system.
Charge the battery, then start the bike (kick), and then make battery voltage measurements at idle, 2000, 3000, 4000, and 5000 RPM.
The stock bike (you didn't say if the bike has any mods) draws about 120 watts with the keyswitch on. The alternator makes about 50 W at idle and 150 watts at 5000 rpm if all is well.
This means if you left it idle long enough, there won't be enough power left in the battery to fire the spark plugs. If you spend more time below the RPM where the alternator does charge the battery vs the time spend at RPMs where it does, the engine will stop.
If you added a higher wattage headlight, you have exacerbated the issue.
perhaps the AC condensor
I never heard of a 550 with air conditioning. Where does the compressor get driven from?
Show us a picture!
Cheers,