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tank suck? is it venting? did you replace the plug wires when you got the coils? you should. are the coils really hot when it shuts down? are the coils the right ones for this bike?I know nothing about GSXR's is there 2 or 4 coils?
Did you accidentally pinch a fuel line when you re installed the tank? Sure sounds like fuel starvation, plugged filter or petcock screen? If all these check out I would be checking carb float levels.
You can put a timing light on a spark plug wire to see if it's still sparking as it dies. If it keeps dying at the same point in time it's either the coils simultaneously overheating and crapping out at the same moment or it's starving for fuel. I'm leaning toward fuel since an upstream fuel problem is more likely to affect all the cylinders at once. Does this one have a vacuum fuel pump? Next time it happens you could shut off the fuel valve immediately and check a float bowl.
From distant memory these things had a vacuum driven fuel pump and activated tap that was prone to issues some of them had a "prime" setting might be worth seeing what happens if you run the bike on that or even check you are turning it on and not to prime. The other thing is the 41mm FCR the carb recommended for the bike? They are capable of massive flow and generally were uses on high performance single cylinder 500cc plus dirt bikes its possible they are too big when feeding a cylinder that's just over 250cc.
The new coils were the issue. And yes, those 41mm FCR's are very much oversized for this type of bike, but I absolutely love the way they sound and perform. To me, listening to those flat slides rattle at idle speed, and then synchronic into a fast almost turbo like whistling sound is intoxicating to me. But, not everybody likes the sounds that the slides make at idle. Some people actually asked be if I had engine problems.... My bike was, and still is somewhat setup for the drag strip. She was raced in her younger years at the Maryland International Raceway in the late 90's, and I bought her setup already with the FCR's from her owner two years ago. I almost pulled this $3k set of FCR's out of this bike, since this bike was a blast to ride at full throttle from 0-200, or at constant speeds over 70mph, but those carbs sucked down way too much fuel and constantly either flooded the carbs out and thereby barking her engine down at City speeds or just simply cut the engine off when sitting at a light. I found a local shop, and they with the help of Keihin / Sudco came up with a jetting setup which allows me to ride this bike now both at low and high rpm's. Needless to say, this bike will not see the drag strip again, and she definitely lost some mid and high rpm torque and top speed, but she still has around 180 hp, and this for a 22 year old bike is not too bad.