Check your fuel cap. When it starts to die out, loosen the cap and see if the problem goes away. If it does, then the fuel cap vent is clogged.
If that's not what's causing your problem, it could really be a lot of things. Normally we see the problem where it dies and won't start for several hours. But for it to start back after just a few mins I would have to think it's a fueling issue of one form or another.The fuel shutoff solenoid could be losing power or coming unplugged slightly. You can check that by pushing the plug (if it has one, some are direct wired) and making sure it's secure. To see if it's working you can turn the key off and on. You should be able to hear it "click" or at least feel it click.