I agree with everything that everyone else said, but will add the there is a good possibility that there is a screen on the fuel pickup in the tank. I highly recommend permanently removing the screen and letting the fuel filters do their jobs.
On both by 80's vintage Sabres, the screen on the pickup becam clogged while underway. When the engine stopped or reduced RPM, the decrease in suction allowed the engine to either restart or increase RPM until the cycle repeated. On my current boat, I pulled the screen during the first month of ownership and immediately sucked a bunch of crud into my Raycor. It's been clean ever since. It's much easier to replace a filter than to pull the screen and clean it!!
I recommend an algicide to prevent algae buildup and a full tank during winter layup (or anytime else) as others recommend.