You have to provide us information in order for us to come to a correct solution. The most important question to be answered is above. I'll repeat it here:
"I'd like to know how this problem came to be. Is this machine just out of off-season storage, or has this developed during regular use? when did it last run correctly?"
Surely you understand that we cannot see/smell/touch your particular machine, and thus what you tell us is all we can go on. It may take a few itterations of test/result/recommendation to come to the ultimate solution.
The history of the problem is the first step. The problem you've described can be caused by a few different things.
If the machine is just out of off-season storage, it's quite likely a problem related to fuel degradation. This can result in simply needing to switch out the fuel, or if worse, can require a complete carburetor rebuild and fuel line replacement.
If it was running fine and just began quitting regularly, it could be another set of issues, perhaps ignition related, or perhaps fuel system related. The fuel pickup could have simply fallen off in the tank, or a fuel line could be pinholed.
Stick with us, we'll solve the problem. If you're in a hurry for easy answers, pay your local repair man instead. He'll do the same thing, but without the time required for the back and forth that solving this by internet forum will require.
Given the chance and a willing OP, our success rate in small engine repair is quite good, and very economical.