It'll stop dead as it's under load of sorts. Electrically, as you say they are simple and if it was an electrical issue you would have trouble starting every time. Check the carb hasn't come adrift slightly and is sucking air, other than that it's getting tired. Local mower shop or Ebay source a carb repair kit strip and sort it. (Item
190556871460 might do the job but you will have to ask them about your model or search for a kit for yours etc) Also source a new air filter and a can of carb cleaner spray and don't prod around with bits of wire in any ports or jets. Change the plug and the oil at the same time. If the plug is fairly black suspect piston rings, but that's usually after many years of use.
I used to look after a small fleet of these little buggers with several el'cheapo makes of two smoke as well which revved like a bugger when the field teams played with them during an 8 hour day. All a much of a muchness really to look after.
My trusty old mower is no longer trusty. It starts OK, and runs for a couple of circuits of the lawn, then stops dead. The stop is so sudden it almost seems electrical, but in other respects it's as if the fuel in the carburettor float chamber has been used up and not replenished - but of course there is no float chamber, and the fuel system looks childishly simple. The electrics are so simple - no moving parts except the magneto - that it's hard to see what could go wrong there either. Maybe there is something about the fuel system that I don't understand. I've taken all the fuel-related bits off, and when I feel inspired I'll take them apart and clean everything. Meanwhile, perhaps someone with experience can suggest what I should be looking for. The sparkplug is new, by the way. It does look rather sooty, but not at the business end (close to the gap).