So what exactly is happening?
the drive slows down & stops ?
or the engine slows down & stops ?
If it is the engine dose it just slowly die or does it dire like it is running out of fuel or like you turned it off .
Being that it is a very old side valve ( L head ) my first place to check would be the valves
Side valve engines erode under the valve and eventually the exhaust valve does not fully close so the engine looses power, runs slower with less power, spins faster when cranking to start and the muffler will usually end up glowing red hot .
As the engine heats up and metal parts expand this gets worse
Checking the valves can be easy but expansive or difficult but cheap
Easy way is to remove the blower housing then remove the head
Rotate the engine at least 2 full revolutions and check that both valves close fully
This will cost you a new head gasket
The hard but cheap method is to remove the carburettor then remove the valve chest cover plate behind the carburettor and check the valve lash
On side valves it reduces over time so the valves can not fully close
If you have access to a compressor you can remove the spark plug put a stick down he plug hole then turn the engine to top dead center ( Piston closest to the spark plug ) then about 1/4" down
Cut a hole in a cork for an air duster shove it in the plug hole and blow compresses air into the cylinder while holding the flywheel so it can not move
If you hear air coming out of either the muffle or carburettor rotate the engine another full turn & repeat
If air is still coming out of the muffler then the exhaust valve needs to be adjusted
To adjust the valves you ned to remove metal from the end of the stem which is require the valve chest to be open and best done with the head off
I use a fine oil stone to remove material off the end of the vale stem, it is a slow job, remove check then remove more & check, repeat, repeat , repeat , till you get to the maximum gap which will reduce when you put the spring back one
The seat usually needs a touch up with some lapping paste
Sounds a lot more complicated than it is
Back in the early 1900 corn farmers who had never been to primary school would do this in their fields
And find a better mechanic