Nissan 3.5 4 stroke will not run in gear.

I have a 2008 Nissan 3.5 hp 4-stroke outboard that has preformed flawlessly for 8 months. It suddenly quit running one day while we were returning to the marina. It will start up, idle, run at 40% throttle for up to 10 mins but as soon as you put it in gear and try to throttle up it dies. Sometimes it will run in gear throttled up at 30-40% for up to 3-5 mins but then always dies. I've replaced the fuel cap thinking it might not be venting correctly and also had a Tohatsu certified repairman replace the carburator with a brand new one and no change whatsoever. I've taken it to two different repairmen and they are stumped as to what the problem is. Does anybody have any suggestions on how to get this motor to run consistently again?
Thank you in advance for any help you might provide.
San Juan 7.7

What is your actual model (not year)? Late MFS3.5B models have a fuel pump and EPA fuel cap; earlier models don't. Has the fuel filter at the fuel cock been checked? After it stalls, will it immediately restart?

It listed as a NSF3.5A 3BR-1. I can't say for certain that the fuel filter has been checked but I will ask my repair tech tomorrow when I talk to him. I would hope he has done this since we have now replaced the carburetor. After it stalls it will usually restart with one or two pulls. Sometimes it takes more. It seems like the longer you mess with it and try and get it to run in gear the harder it is to keep it running and restart. If you simply idle the motor up in neutral it will run for up to 10 mins with an occasional hitch that it usually recovers from.

Sounds like fuel flow restriction. Enough to idle, but not much more. The fuel filter is inside the fuel line, at the fuel cock inlet. Might be restricted. Also the tank needs to be full, and the motor not tilted too far, or the gravity feed will not get enough gas to the carb.

I've asked the tech who replaced the carb about the fuel filter and he seems to think there is not one. Also he said there was no sign of debris in the carb he removed. I am taking the motor back to him in the next couple of days and have asked him to recheck and possibly replace the fuel line.
The motor has run perfectly for me for 8 mts before starting this behavior suddenly with no notice. It's a very low hours engine that looks brand new which makes this that much more furstrating.
Thank you for the suggestions Paul. I will let you know what I find out.