Yes tank vent has to be the first thought, including does it actually allow air in when you open it.
Further random thoughts.
I think the cooling water is ok, most models have it escaping other places than the tell tale and exhaust. I guess not but does your model have either low oil pressure or overheating cut outs?
Have you tried pumping the primer as it dies? Spraying some fuel or easi-start in the carb as it dies should prove a fuel or spark issue. If fuel you need to prove the supply is ok… tank, hoses, primer. Then think about the fuel pump and carb.
Ign issues are less likely but I have experienced failure of ign components due to heat soak.
Worth checking the kill cord/stop switch isn’t suffering a random failure
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