Check the linkage under the cover for the throttle cable from the hotfoot. It might be loose. Not real likely, but this is somewhat similar to a problem I saw a while back where a nut had come loose on the throttle cable. It normally would make it hard to start all the time, or over or underthrottle, but just to be sure.
Next, check your ignition wire harness from behind the key on back past the hotfoot for breaks, loose connections and bare/rubbed wires - especially if the wires lay over any of the steering system or other metal. This could cause an intermittent short that will only get worse. You might not get spark at the plugs if certain wires are shorting out.
Check the kill switch for loose, rubbed or broken wires. A bad kill switch might also cause what you describe.
It is more likely wiring related than actually a problem in the motor. These are all the ideas I have from problems I've seen on various motors with various anglers in the past.
Giving it gas with the hotfoot may or may not be related, but if it isn't one of the problems above, someone more mechanically inclined with the actual motor than me is needed. If I think of anything else, I'll add it here.