Hopefully your technicians have checked the engine set-up and have made sure the pick-up or idle timing is correct and the carburetor linkages are set correctly. I am guessing this is a 2-stroke engine and that the possibility of contaminated fuel has been ruled out. If idle timing is correct and your gas is perfectly clean. Your problem may be that the carburetors are adjusted to lean and may need the idle mixture to be richened up a little.
How this could cause your problem is if you slow down and then quickly accelerate again there is enough residual fuel in the crankcase that the engine will not stall. I am assuming that is what your engine does. After the engine has idled for three or more minutes the extra fuel is gone and because the idle mix on the carburetor is set to lean the engine dies on acceleration because the fuel is not being supplied fast enough. By you activating the primer you’re supplying the extra fuel.
Things you need to be aware of when the idle mixture on your engine is adjusting. If the engine is being adjusted with the engine simply running on a hose with muffs the back pressure on the exhaust will be incorrect and this could cause the mixture to be set incorrectly. If the engine is being run in a test tank make sure the water level on the outboard is similar to what it would be if the boat was in the water and that the water temperature of the test tank is close to the temperature of the water the boat is normally operated in both of these item affect idle mixture adjustments. The best way to adjust the carburetor is have the boat in the water and if possible and safe put the engine in gear.
Last thing make sure your idle speed is not set too low. Sometimes guys like to have low idle speeds for trolling. The idle speed adjustment is there to keep the engine running properly it is not a troll control. Hopefully this information is helpful.