What exactly is the sequence of events for it to fail? Does it only stop after running at WOT or does it just do it after time?
If the engine dies at WOT and you have to prime it (or crank it for a long time) before it starts, this could be fuel starvation and the carbs have been emptied by basically the engine being unable to suck enough fuel through the system. Could be chocked filter, dirt in carbs, dirt in fuel pump or elsewhere in the fuel system.
If it's completely random, it could be water (as Chris suggests) or dirt in the carbs. If it's an old tank and there is dirt or water in the bottom of it, this will eventually get sucked through the system to some degree and would also cause problems. is the tank clean?
Do you have an inline water seperating fuel filter (not the one on the engine)?
Some more info would help diagnose a bit better but there is always going to be a bit of testing to get to the root cause. If it's not the tank and / or fuel hose, stripping down and cleaning the carbs, pump and fuel filter may be a good idea if it's not been serviced recently. If you're not confident doing this, throw it at a service shop who will also set the float height and sync the carbs for you. This may also help restore some of your confidence in the engine.
As per my other post, renewing the tank and fuel hose need not be an expensive exercise and would at least guarantee that that's not at fault if you are in any doubt. A leaking fuel tank will let fuel out but also potentially water and dirt in, especially if it's sitting uncovered in the rain.