I have a 99 CBR 600 F4. It has 25k on it now. I bought it with the knowledge of this problem. The bike runs fine down the road until it gets warmed up. I will be driving at coast speed of 50 mph in fourth gear at about 4-6k rpms. The bike suddnely starts to cut out. I sounds like it is suddenly runnng out of fuel. If you give it throttle, It bogs more and more and keeps losing rpm until it stalls completely. I pull to side of road and choke it full. The bike starts up again and goes down the road like nothing ever happened. 5-10 miles down the road, it will do it again. It doesn't matter what gear Im in but does seem to happen only in that lower rpm. It only does it when Im cruising and then get back into the throttle. I pulled off the gas tank, emptied it and pulled off petcock and cleaned it with carb cleaner. I also took off air box and opened up to check air filter. The filter seemed like it was soaked with fuel. Not so bad that it was dripping fuel, but had a strong smell of fuel. There was also fuel residue around where each carb attaches to the air box. The only one that was dry was #4. Are my carbs out of synch? Are the valves in carbs sticking? Should I clean the carbs, including jets and all? I am getting a new air filter as soon as possble. I put back together today. I mixed 91 octane, non ethanol gas with seafoam in clean tank and took for ride. Now bike hesitates on acceleration. I didnt ride long enough to see if it would cut out. I was scared to do damage to bike. Can you help me out? Bike had new plugs, in line fuel filter, fuel relay. How about the regulator rectifier? Is it getting too hot and not working? The bike wont start back up without the choke though...

 

Pull the carbs and clean them, then sync them.
Be sure to clean all the fuel lines too.
Check the air breather into your tank isn't blocked too.

 

You say the fuel pump relay was replaced, which would been my first check. Do the fuel pump flow text after its gotten warm and preferrably when it starts acting up. The fuel pump may be going. also check any fuel filter, and check the fuel line from tank to carbs. I had to replace mine on the f4, and I got same diameter fuel hose but not the factory preformed. It was a little to long and would bump the frame at the tank mount and pinch off. It would get just enough fuel to get going and the starve out. I rode it under 60 for 30 miles till i got on an interstate and thats when it started cutting and I found the issue.