Just a thought. This will happen if the coil is kaput. The insulation breaks down when it gets hot. Could you get the coil tested at say a lawnmower or motorbike repair shop?
If you are getting reasonable waterflow (around pencil thickness) out of the engine the impeller is probably ok
I might be wrong but it could be worth checking. It happened on my seagull last year and with a replacement coil it is back to running all day no problem again
You can check the resistance with a multimeter but it isnt all that effective. Maybe you can find a cheao replacement coil on ebay
All the best. Robert