Ok first of all I'm not sure what the solution or problem is...but I had the same thing happen last year on my 2001. Stop and go traffic bike constantly overheating, cutting the bike on and off, and finally the bike didn't start at all.
Ended up being my starter gears were shot but it was covered in a Suzuzki "notice DEC 12 2002" so they fixed it for free with a new starter even though the bike was out of warranty.
A couple of things I've noticed before and since
1. 1298 cc's covered in plastics doesn't work well in stop and go traffic because of overheating...... What I did and am doing is this 1) flushed my radiator and filled it with Dave's engine Ice 2) wrapped my headers to reduce ambient heat under the cowling 3) added a muzzy fan 4) adding and aux switch controlled radiator fan in the upcoming week. Even without the fan I haven't overheated as of yet and have had no starting problems.
2. Check your battery one thing to realize (someone correct me if I'm wrong) the alternator doesn't kick in and start charging the battery till somewhere around 3500rpm which means if you are in stop and go traffic the battery isn't charging and you are still running the engine, lights, etc so you're draining your battery. Then if you are cutting the engine on and off againin the traffic you've just added to the problem.
3. Check your battery, what kind of condition is it in and how long have you had it? I've heard batteries lasting from 1yr to 5yr, with the avg rider changing theirs about every 2years or so. When you aren't riding keep it on a battery tender to insure the battery is always up to a full charge. If not and its not if you hit stop and go traffic before you had a chance to run it up and start charging it you are going to be sitting on a busa in the heat, lights on , fan running, with a battery thats not fully charged with a bike that has a heavy duty starter (2003+) thats gonna suck the life out of it every time you hit the start button.
Hopefully if this doesn't really answer the question it give you some info to avoid having to ask it or live through it