Volvo Penta Engine Shuts down

I have a 2004 Volvo Penta 5.0 GL inboard engine. I just bought the boat a few weeks a go. The 1st time we took it out, it would run consistently if we were zig sagging but, when we ran it in a straight line for more than a few minutes It would shut down. I chalked this up to possible water in the gas. I bought some fuel stabilizer. We took it out again the next day and ran it for approximately 2 hours and it only shut down on us once and started right back up. It sat for 2 weeks and we took it out again. This time, it ran for approximately 30 minutes and shut down. I kept trying to restart it. after about 10 minutes it started back up but only ran for about 3 minutes and then shut down again. I tried to restart it for about 10 minutes and it wouldn't restart. finally had some one tow us back to the ramp. Once at the ramp, I tried to start it again, it started back up but only ran for a few minutes and then shut down again. Today, I tried to run it out of the water with the ear muffs on. It's doing the same thing. It'll run for 20 minutes or so then shut down. I can restart it but, it will only run for a minute or 2 and then shut down again. Any ideas??

I have a 2011 4.3 I/O and my engine doesn't completely stall, but the warning alarm from the engine starts beeping is telegraph message and engine protection mechanism prevents me from going faster than an idle. I am told by the marina that it is stumped trying to find explanation. The sensors seem to be working, the engine is not too hot (the problem often arrises at the start of day). By process of elimination they think it may be a faulty computer; $2500 to replace.
Please advise. Has anyone else out there had the same problem and if so what was the solution?

I would look at the fuel filters to start.