I have a fuel pressure guage set coming to test that. If it does lose pressure, then it could be either the low pressure pump which fills the FSM, or the high pressure pump that feeds the injectors. The other thing is the float switch might be faulty / sticking in the high position thus shutting...
My 2008 Merc 90 4 stroke EFI will start fine, idle great but after a minute or so at full throttle will fall flat on its face. It’s like I pulled back on throttle to neutral. Once that happens it runs rough and then run fine. Idle for a couple of minutes then full throttle, it does it again...