Follow up...There appeared to be no stuck valve. The engine had cooled some before I investigated that.

I'm thinking that an intake valve may be sticking open...how can I verify that? If there is varnish causing this, would something like Marvel Mystery Oil possibly help? I have run Mobil 1 Synthetic since new.

Thanks.

When this problem occurs, remove both spark plugs & check for spark on both. Then check compression on both cylinders. Report your results...

Marty

Will do. Thanks.

Is this "running one cyl." a new thing or have you been chasing this for a while? If this were due to a sticking intake valve, adding Marvel Mystery Oil AND Seafoam to the fuel supply might help prevent that from happening.
***"I'm thinking that an intake valve may be sticking open...how can I verify that?"***
Verification of a sticking valve COULD be had by removing the valve cover from the affected cylinder BEFORE cranking the engine. Then, with the valve cover off, carefully observe whether the intake valve is being held down by the rocker arm. If you see that the engine stopped with the intake valve down (open), turn the engine by hand in the correct direction of rotation while watching the action of the valve train. If the intake valve does not begin to rise (closing) as you turn the engine, push down on the rocker arm where the pushrod is located. Push as if trying to move the pushrod toward the camshaft. When you do this, if the intake valve is stuck open, the clearance between the end of valve stem and the rocker arm will increase. Keep your fingers away from the end of valve stem, if the valve is stuck and suddenly breaks loose, it could be painful for you. The thing about an OHV engine intake valve becoming stuck open when not running is that it requires the engine had to stop when that cylinder was performing the "Intake Stroke". If the intake valve sticks open, as soon as the engine begins to crank, it rotates to the next stroke (Compression Stroke) and the camshaft begins to lower the pushrod which allows the intake valve to close. IF....the intake valve sticks "open", it will be struck by the piston as the piston moves upward during this compression stroke(OHV engines only). When the piston strikes the intake valve, it knocks the valve free, provided the pushrod has not gotten between the edge of the rocker arm cup that retains the pushrod. If the pushrod has stayed within the confines of the rocker arm cup, there may be no damage to the valve or to the pushrod. However, if the pushrod manages to get onto the edge of the cup, when the piston strikes the valve, it will bend the valve, bend the pushrod, break or bend the rocker arm......or any combination of those possible damages.

Mownie, This has been going on for a few weeks...it's very frustrating. I am by no means an expert on small engines. What do you think may be happening? Valve train or electrical?

Thanks,
David

Kind of tough to make that call without a working compression test of when the problem happens, compared to the compression reading when it is running both cylinders.
When you "switched the coils", was this a complete assembly swap (including the high tension spark plug cables)? I presumed the coil and spark plug cable were inseparable, but you never know? It sure would be helpful if a diagram of the ignition system could be viewed.

Mownie...Re: Switching the coils: Yes, the coils are a complete assembly that have the plug cables attached. I could not find an electrical schematic to post. Will try to get a compression check soon and post results.

I have read some of your posts about the seal between the carb and intake allowing particulate to be introduced into the combustion chamber...would problems related to this show up well before 625 hours or is this something you think I need to look at? I have kept the machine regularly serviced since new.

Thanks to everyone for their help!

David

***"seal between the carb and intake allowing particulate to be introduced into the combustion chamber"***
That defect could not manifest itself as a problem with just one cylinder (in a multi cylinder engine) unless the engine also featured an individual carb for each cylinder.
If your engine had that problem, it would likely have demanded attention because of oil consumption or significant reduced power/reluctant starting. Also, if an engine is fed a diet rich in dirt, the wear-out of the upper cylinder components can occur in a very short period, depending on several factors.
I guess I'm just not too savvy in getting useful info from the deere.com website, I can't even find any info on the Deere 335 by going to the Deere site. So, if somebody on the forum can steer me toward an IPL for this 335 w/Kaw twin, I for one, would appreciate it. I'm sort of leaning toward a problem in the ignition system that could cause the same cylinder's coil to be "killed" by the fault, without affecting the opposite coil.
It is a bit of a "long shot" that the problem might be due to a problem in the valves of the affected cylinder. The only thing I can think of that could possibly cause the left cylinder to cease operating after being shut off hot would be if the exhaust valve had insufficient clearance. Exhaust valves take a real thermal beating, they are literally washed in hot exhaust gases, with very minimal cooling afforded in operation. Intake valves, however, get cooled by the cool induction stream entering the cylinder.
IF.......the exhaust valve of the left cylinder had too little clearance, that valve might be overheating enough from latent heat soak after a hot shutdown, to expand and prevent the valve from seating under those conditions. It will be a good idea to properly check the valve adjustment at this time. And, as I said, this scenario is somthing of a long shot, valves that run with too little clearance and consequently overheat, will usually give symptoms of "fading power accompanied by a misfire" DURING operation, not after it has been shut down and restarted. But, when dealing with an issue that is "not typical", it's best to leave no stone unturned.

** Follow Up **

Turned out to be a bad coil. Evidently when I thought I switched them I must have put them in their original position. Yesterday when mowing, the engine started running on one cylinder...first time this had happened while the engine was running. Checked compression - it had some (thumb over the hole method, lol), no spark. Switched coils and the problem moved to the other cylinder.

Thanks again to all who responded. Y'all are a great resource!

David