Start with the basics. As soon as a motor shuts down check spark and fuel pressure. At least that will give some direction. Most fuel pressure guages will allow you to take a fuel sample with the pressure release hose, make sure there is gas not water there while it's not starting. It may be there is water in the tanks that only gets sucked up when the boat is off plane and low in the rear, then rolls forward when on plane.

Thanks I will try that. I talked to Bruce today at Sonic. He told me that he talked to someone at mucury and they said they think it is vapor locking. I don't know. we are running out of good wheather here in Pa. I hope to fix it before winter.

check for a cracked coil. I had similar problems on a HP500-was very intermittent. When coil got warm the crack would open and get a spark to ground. Engine wouldn't give me rpm then and eventually just shut down. When engine got some cooler air would start and run fine until next heat up.
Crack was not visiible to naked eye. Only detected by hearing a cracking sound (arcing) and then darkening engine compartment and could then see the intermittent arc.

Thanks for the info, I think we may have figured it out, But I can't find out now until spring. I took it to get winterized and found that the motor with the shutting off problem was not charging and one battery was dead. my tech thinks that both motors could not run off of just the one charging? well new alternater later now I'll have to wait for warm wheather to find out.