Difficult to start warm 50hp 4-stroke

I have a 2001 T50. The engine starts quickly after sitting overnight or sitting for a couple of days. It runs fine at idle and at WOT and every where in-between. But, after running a while and then stopping and letting it sit for a few minutes or longer, it may start right away or it may take many tries to get it running again. Squeezing the primer bulb or using the automatic choke with the key or increasing the manual throttle speed seems to matter little. The boat has a 24 gal fuel tank.

I recently had the engine serviced - new plugs, oil/filter changed, new fuel filter and timing belt checked. The problem existed before the service and still behaves the same after the service - the service does not seems to have made any difference.

The engine always does restart but sometimes it may take several minutes of trying to get it running again (occasionally up to 15 minutes of trying to start it)..

Does this sound like something that is common - thus there is a solution, or is this problem so vague that it does not have a simple recommendation for a fix?

Thanks

In doing my research, it seems this condition is not as uncommon as I thought. I've read other posts with this same problem - engine starts easy when cold, but is difficult to re-start after engine has been running. The engine hp range from 9.9 to 250 but all seem to be 4-stroke.

So there must be some common factor(s) - fuel, electronics, ???

What happens when the engine is warm that does not happen when it is cold that would make the engine harder to start in a 4-stroke?