OK, I assume when you try to re-start the engine after sitting, that the starter cranks over the engine. Is this correct?. If the engine cranks but will not start you need to check a few things. Make sure you are cranking fast and not just turning the engine. You could have a weak battery that is not be charged while you are underway and is not cranking fast enough, but recovers overtime.
1. While you are cranking, do you have spark at the plugs. If you do not, you may have a break in the plug wire that gets worse from the heat generated when the boat is running, or some other electrical problem exists.
2. If you have spark at the plugs, pull the plugs after trying to restart. They should be wet if you are getting gas to the cylinders but not firing. If they are dry, you are not getting gas. You could try pushing the throttle handle forward a few times to activate the pump.
You could also have a vapor lock. A vapor lock is where the gas in the lines evaporate from the heat when sitting and you lose prime on the carb. When the fuel cools off it returns to liquid.
These boats do not use a positive pressure pump, rather they use a diaphragm in the carb or on a external pump to pull fuel in. If this diaphragm has a small hole or is weak, it may not be strong enough to overcome the vapor lock. You may also have a small leak in one of the fuel line connections and sucking in a little air. This is a more common problem on engines where the tank and fuel lines are exposed to the heat of the sun. That is why outboards use a primer bulb.
You need to determine if your problem is fuel related or spark related. Once you figure out what is missing, then you can narrow down the search for the problem.