One of the things that cause the mower to run poorer, start harder,
and finally stop is a plugged air filter. I've seen this a lot,
20% of dead mowers - especially the classic Briggs and Stratton engines
Out of sight, out of mind. The mower looks nice and clean, but
look at this mess, the engine is trying to inhale air through this!
The foam comes right out. This is plugged.
So what I do is fill a coffee can with hot water and a little dishwashing soap. Clean off the foam, wring it out, and put just a little motor oil (or the official filter stuff) on the foam. Wring it out again and reassemble.
Ought to look like this, it will probably run now.
HOWEVER, if the filter was plugged up like that it has probably fouled the sparkplug (which will also need cleaning) and in some cases will even start sucking the oil out of the crankcase!
Here's an impressively plugged
side flow air filter
Here's the all time record for plugged air filters!
This is a close second in the furry category!