Does it "wheeze" when it dies? We have had periodic problems over the years with one of our 5 hp nissans and always found some crud in one of the jets in the carb.
Don't think it's necessary to get a carb kit unless the engine is quite old. Pay attention as you disassemble it, don't lose any bits, and take out all the jets, inspect them and blow them out. As long as you haven't damaged the gaskets you should be able to reassemble it and be good to go for a while.
Very simple engines, most likely a carb problem.
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)
1984 Fast/Nicholson 345 "FastForward"