So which valve's pushrod is dying?
It's on the inlet side. The exhaust has the steel rod.
So which valve's pushrod is dying?
Measure the height of the valve guides, they should be the same.
What is happening is the pushrod is dropping into the engine then the cam comes around & breaks it
The push rods jump off because the valve lash gets too big
The plastic guide that is there need to be replaced , where is the other one ?
Do not reuse the old head gasket.
There is way too much oil in your head so most likely the valve stem oil seal on the inlet valve is gone ( none on the exhaust ).
Were both of the lash caps on the end of the valve stems ?
If one dropped off
1) it will be in the engine somewhere
2) puts the rocker at an angle where it can hit the valve spring which can cause the push rod to drop off.
I've attached another photo here - this taken prior to disassembly but with a new pushrod trial-fitted to check the clearance.
Looks like the rocker retainer nuts are different between then intake and exhaust. Could the larger looking nut be causing binding of the intake rocker leading to excessive wear on the intake aluminum push rod.
IT is sounding more & more like a loose valve guide.
Give each one a LIGHT tap using a drift to prevent damaging the end.
If the inlet moves even the tiniest amount then it needs to be repaired.
Walt has a system that seems to work fairly well, or just replace the head.
The valve guide should not exceed 1/8 inch above the head casting. It is quit normal for the aluminum push rod to wear thin and bend when not rotated end for end periodically on this engine when adjusting valves which should be done every year per B&S but a couple years at most. Replace it when the push rod shows heavy wear. As said above, many have replaced the aluminum push rod with the steel one with no apparent problems. Note that the later version of this engine uses a different assembly support method eliminating this wear problem.
No clearance when new push rod installed - check that the push rod is seated in the recess in cam follower, tappet.
Walt Conner
Thanks. The thing with this engine is that the pushrod was new last season, after suffering a similar break last year; until then it had been fine for a dozen years or more.
I've now replaced the whole cylinder head with a good second-hand part, and it seems to be working perfectly. Interestingly, the rocker (which was previously at an awkward angle) is now level.