Might I ask what the shop has already tried to fix?

Sounds like a carb issue (you mentioned old fuel)

Might also be a weak governor spring.

The garage, (local, well recommended, repairs all the local lawnmowers) cleaned and adjusted the carb, blew out jets. I think he had spent some time it even though he didn't charge me. We have put more fuel in the tank but didn't clean out the old because I hadn't heard about what happens to old fuel left standing until I read about it on this forum. Would it be worth draining down the fuel and then running some sort of flushing through it. I am not mechanically minded so don't know whether that is feasible or not.

You could try replacing the fuel and get it up and running- then feeding bursts of spray carb cleaner down through the carb throat as it runs to help remedy a s sticky valve issue. Very common on these after they sit. On these there have been several that even look clean inside, but pull them apart and blow them out they don't perform right. New carbs are ridiculously inexpensive. So I would pick up a new carb, gaskets, remove the tank (via the three recoil bolts) clean it and flush the line and there ya go. If the tank is real dirty, don't be afraid to simply wash it well with water and let it dry. Otherwise, a few rinses w/ clean fuel is normally what it takes.

"Would it be worth draining down the fuel and then running some sort of flushing through it. I am not mechanically minded so don't know whether that is feasible or not."

I'd drain out the old fuel.
IF your carb has the bowl drain nut, open that too so everything drains.

Put in about 0.2-0.3 liter of fresh fuel.
Add a STRONG amount of carb cleaner to the fuel. About 10x the recommended amount for "normal" use.
Run the engine to use up the fuel. Hopefully it'll start to "improve" in a short time.
When the engine is running well, top off the fuel tank and run a few minutes to dilute the strong carb cleaning solution from the fuel lines etc.

Also make sure the fuel shot off valve id FULLY open.

Thanks for the replies, all very helpful & interesting, how did we all manage to learn anything before the Internet !!

I'd also clean out the muffler.

I've also heard of poor ventilation with the gas cap to cause similar things.

And there's the fuel filter, too.

FYI I had this problem w/a Briggs engine. Try this:
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Scotts Riding Mower w/25HP Briggs Intek. Hard start and surging then just dies out. I have had issues with this for a long while. It normally went away when warmed up. Now I could not keep it running. It would run if I kept spraying in starting fluid. But then just stop abruptly. Did carb cleaner; same. I was reading up on governor issues, so I went out and spayed aerosol "dry" lubricant all over the gov. & linkages twice. It started and ran perfectly now. Seems like that was the issue. The gov. was not responding properly to keep it running. I have not used for a job yet, so I will see if that really cured it...