Sounds like the impeller is becoming airated. In other words, air is being sucked during acceleration from inside the hull into the impeller causing it to "slip". Or, it's possible the wear ring around the impeller is damaged enough to allow impeller cavitation.
The problem alleviates as hull speed increases, right? Initially, the differential pressure across the impeller and internal of the tunnel are quite negative during acceleration thus air leaks at the drive shaft seal inward to the tunnel and/or impeller wear ring condition are dominant factors. As hull speed increases the pump inlet pressure actually becomes positive thus the differential pressure drop across the impeller becomes less critical and/or air is no longer being sucked into the tunnel negative pressure zone from the inside of hull through the drive shaft seal.
Pump malfunction can also occur in some cases when a plastic bag for instance, is sucked into the jet pump and gets stuck behind the impeller but in this case the boat cannot accelerate enough to reach the point of speed where the pump becomes loaded and less likely to suffer from air leaks or cavitation. In this case the boat simply cannot reach cruising speed due to the obstruction.
Thus, grab a flashlight, look into the pump inlet and outlet for signs of something clogging the flow path. Also, inspect the annular wear ring around the impeller for gouges and or physical damage, the gap between the ring and impeller blades must be very small, much less than the thickness of a dime is probably good.
If all of that looks okay, I suspect your carbon drive shaft thru-hull seal is worn out, this happens more rapidly when the engine is run out of water such as on a flush hose.
Assuming this is a 4-tec that is, not a mercury powered sportjet.