Make sure the vent in the fuel cap is open.

Check for spark.
I recommend checking for spark when the engine is cold so you have a reference to what "adequate" spark looks like.
Check again when it fails and compare.
Sometimes coils (armature) can get heat sensitive.

Thanks, Bill. I will check the spark with the engine hot and cold. The fuel cap vent is fine.

I have checked the spark when hot and after running for a total of ten minutes (in short periods as it keeps stopping and then is restarted by priming three times). It runs well for a minute or so but then starts to miss and then gradually come to a stop. The spark is fine both hot and cold.
I now strongly suspect the diaphragm in the carb because another symptom is that the primer bulb gradually gets sucked in as the misfiring starts. When the engine stops the bulb gradually comes out to its normal position.
So do I put a new diaphragm in and if so please would you direct me to a site which will tell me how to do it?

3.75 Briggs carb rebuild

This is an easy DIY job to replace the diaphragm of the carburetor. A damaged diaphragm will cause engine surging, hard starting, and erratic high speed operation. You may also notice that the primer bulb isn’t working properly.

{{gwi:127520}}

This is an overview of the carburetor and these types of carb-over-tank are typical of small Briggs engines. Note the two governor springs. The carb/tank assembly is held in place by a ½” bolt to the left of the carb and a 3/8” bolt on the engine head to the right. Remove both bolts and pull the tank straight out with a rocking motion. If possible, the carb/tank assembly should be blown off with compressed air and all loose dirt removed. Use the proper safety equipment, especially safety glasses, before using any compressed air in any of the steps below.

{{gwi:127521}}

In the highlighted area you will see the governor linkage still in the throttle plate of the carburetor. You will have to gently separate the carb/tank assembly from the linkage. It is a Z type linkage. It is not necessary to remove the springs or the other end of the linkage, from the governor.

{{gwi:127522}}

Note that on the rear of the carburetor is found a white plastic ring and O ring. Sometimes these remain on the tube of the engine housing. If so, place them back into the carburetor body, as shown, before reinstalling the carb/tank to the engine.

{{gwi:127523}}

Note the raised area of the diaphragm. This is caused by age, but more often, by ethanol fuels, which damage the diaphragms. A damaged diaphragm will cause engine surging, hard starting, and erratic high speed operation. You may also notice that the primer bulb isn’t working properly.

{{gwi:127524}}

Shown here are the dip tube, which brings up gas from the tank, in the bottom left corner. Just behind that and partially obscured, is the orifice that compressed air can be used to clear the dip tube of debris. It also leads to the primer bulb, so any air must be low pressure and the primer bulb must be held in the depressed position to prevent it from blowing out. In the center top, you’ll notice the jet, surrounded by a wire mesh filter. In the bottom right is a spring. Be careful to not lose the spring or forget to install it during reassembly.

Remove the old gasket and diaphragm combo from the carb body. Install a new gasket/diaphragm on the smooth surface of the tank. I always blow out the tank with compressed air to remove dirt and any water. Be aware that there may also be old gas in the tank. I always empty the tank and let it sit in the sun until all the gasoline evaporates before applying compressed air. Align the carb and lower it down on top of the gasket, trying to keep the five screw holes in the gaskets aligned. Insert the screws and partially tighten them and install all five screws. Tighten each screw until it gently bottoms out. Then turn each screw another quarter turn. It is not necessary to use more than a few inch pounds of torque on these screws. Reinstall in reverse order. When installing, be sure to engage the breather tube with the rubber piece on the carburetor.

Impressive baymee!
It's a shame this forum doesn't have stickies.

I used to do this sort of thing for a boiler manufacturer and I love doing it. I keep all these rebuilds in a file on the computer. Thanks.

Interesting about the boiler.
I used to be a Boilermaker a Naval Shipyard. (PSNS)
Completed my apprenticeship in 1971. Found a "clean" job in 1980.

1971 found my ship in Curtis Bay, Baltimore, shipyard for overhaul. I remember well the welding fumes coming up from the hold.

Thank you baymee. Your text is clear and your photos even better. Now, I will enjoy doing this little job and have noted your comments on careful torqueing the screws. Thank you so much for your trouble in posting it all.
I guess you're used to temperatures in the 90's in Pennsylvania. Its been like this In the UK for 3 weeks now and gardens are dry as dust here in Surrey, 10 miles south of London.
I've spent $2500 on a vacation in Croatia so we could get some sun before winter but I reckon we've had enough here and it was a waste of money!

I really liked England when I was stationed there. So nice and green. Been to Bournemouth couple times vacationing while in country and of course went to Wimbledon . They had just started to build the tunnel to France when I left. Nice people really enjoyed my tour over there.. Tried to play English Snooker! way too hard for old eight ball shooter on them long tables, especially the Looooooooooong shots with the small curved pockets...

Thank You Baymee. Good reference to look back on. Now I know the correct names to some of the parts I've been calling thing a ma gigs :)

Hi. rcmoser! I live only 5 miles from Wimbledon and my son is only walking distance from the tennis club. My sister and brother in law live in Poole, 2 miles east of Bournemouth!
Its a small world and England is Very small! Thanks for coming over. Chris

Sorry, got my east and west mixed up. Poole is just west of Bournemouth!!