It's a shame no one got back to you earlier, the North hemisphere is off season so I guess no one will get back to you in a while.
What you have my friend is a classic case of gas tank vacuume lock. Some models had the gas tank vent and overflow built into the cap or somewhere in the tank.
To diagnose this; when you loose power and pull onto the side, don't wait for a few min, open the gas tank cap right away and you will hear a air rushing sound into your gas tank, straight after you should be able to start and later on it will come back again.
If so then you will have to late the air vent and unblock it, either on the gas tank cap or the gas tank. Which depends on your model.