The seat switch is out of the loop whilst the clutch is pressed. So if the condition occurs w/ the clutch in- you need to look elsewhere. Or does it die once the clutch is released? Water in the fuel system possibly? You may want to post engine #s. A quick glance showed a Kawasaki. Try to give more details if you can on how long it is running, whatever else you've got.

You might be on the right track with the seat switch, but you have no evidence to this point.

Unplug & replug the seat switch connector.

IF it's unplugged, you pretty much guarantee it won't run.

So, I replaced the seat switch and nothing changed.

I then disconnected the battery and removed the fuel shut-off solenoid from the bottom of the carburetor.

I used the battery to test the switch and the plunger drew in when 12v was applied. However, the plunger was very sluggish retracting. I tried to remove the plunger to clean it with carb cleaner but this model of the Kohler fuel shut-off solenoid does not allow you to disassemble it and clean the plunger. I cleaned it as much as I could and re-installed it, and the engine still died just after ignition was successful.

Next I looked on line for a new fuel-shut-off solenoid and they are going for $60 or more plus shipping or local State sales tax.

After wasting money on the seat switch (my fault, I know) I thought that I would check to seeif the fuel shut-off was really the culprit. Therefore, I removed it and cut off the plunger rod, reinstalled it with Never-Seez on the threads, and did not attach the positive wire to it.

The tractor started with no problem and remained running.
Now I have a few questions for Bill and Tom. Can I just leave this fuel shut-off disabled? If so, do I need to install a manual fuel shut-off on the fuel line or is the float in the carb sufficient to stop fuel from flowing when the engine is off?

I also want to mention a few other things. This engine has backfired for two years since it was new, so the plunger solenoid must have been defective from new. This seems like a bad design to me, that is, with a plunger like that at the bottom of the carb bowl with electric current running to it.

Second (and maybe not related) the spark plug was completely black, unusually carbon-ed up, as though fuel was somehow getting in the oil or something. Any ideas as to why the plug was fouled up with black soot so much? I have to admit, that was the first time I changed the plug since it was new almost 2 years ago.

Mechanically speaking, disabling that solenoid won't have a connection w/ flooding when sitting. If the fuel tank is under the hood, an inline shut off valve used properly will be a cheap insurance policy against fuel bypassing the float valve when not being used. What are engine model and spec #s? HAs the air filter been changed yet? Are there signs of fuel in the oil/ IE smell and high level?

Carb fuel solenoid doesn't have a thing to do with fuel flow TO the carb. The "pin" just blocks the main Jet when "off" to prevent afterfire (backfire).

Didn't you even think to look how it could possibly interact with the float/needle & seat
You just ruined a carb solenoid for no good reason.

You still haven't answered the question of "does it die when releasing the clutch"?

Tom:
The air filter was changed after one year, but it looks clean so I did not replace it this year (you could easily see light through the translucent white paper).
This is from my owner's manual: TRACTOR - - MODEL NUMBER YTH21K46 (96045002600), PRODUCT NO. 960 45 00-26
ENGINE.
As far as my concern with fuel possibly getting in the oil, that is solely based upon my observation of the spark plug which looked and smelled like it came out of a ten year old engine that never had the plug changed.
{{gwi:358458}}

Bill:
For whatever reason this particular fuel solenoid interfered with fuel flow because it was not working properly.
The engine would die just after starting, and that is with the clutch pushed in, the blades not engaged, and my fanny in the seat.
As far as ruining the part, I was not worried about that since it did not work properly. The apparent purpose of the part is to prevent backfiring when turning off the engine. However, it never did that so unless there is some other purpose for this solenoid I am not planning on replacing it. Instead, I will install a manual shut-off valve.

kachinee - the black fouled plug indicates the engine has been running with a too-rich fuel mixture - routinely operate engine at full throttle but with choke off.
Also chk:
With choke control set to off at the control panel, look directly down the carb throat with the air filter removed and the choke butterfly plate should be positioned vertically (full open). If your machine has a combination throttle/choke, make sure that the choke is NOT engaging (starting to close or closed) when the throttle is set to highest RPM.

rcbe:
Thank you for your post. This is the typical combination throttle/choke and I pretty much operate it at close to full throttle. I will check to see if the choke remains open as you suggest.
Further to your point about the rich fuel mix, the air filter looks so clean after running the machine for two seasons that I am now wondering if the design of the air filter housing prevents sufficient air from getting to the carb.

I really can't tell from the pic that the plug is actually fouled. Where you get concerned is if there are big enough deposits to misfire the plug. A black coating may be an indicator of a too rich condition. Some just do run black. On your engine, are you running it with a pre-filter in the air box? If so, is it black or green? Black are the newer, less restrictive ones. Some engines were not spec'd with them. If it were mine, yes I would install an inline shut off valve on this application. That is if you don't mind using it.
One other thing to add seeing as though you do your own maintenance. At your main maintenance interval, get in the habit of removing the shroud (4- 8mm or 5/16" head bolts) and do an inspection. Put a 10mm wrench on the top cover bolts and confirm they are tight ( especially the 5 closest to the front of the engine). If these bolts come loose you will likely develop a cracked block. The other bonuses are that you can ensure the cooling system is clean (mice like these too) and the spark plug is an easy change.

The quickest test to tell if fuel is leaking into the oil is pull the dipstick and look/smell.
If the oil level is "growing" or the oil smells like gasoline.