Update: I had the clutch problem yesterday. I left the mower sit overnight. After I revised the post this morning, I restarted the tractor and tried the mower -- bingo! It mows. I finished the yard without disengaging the clutch, then shut off the mower and tried to reengage it. Zip! Nada. No go. Nothing happens - it is like the original problem. I now assume the clutch is the problem and it has something to do with heating up after use. That seems more likely than a bad PTO switch. Comments?

Looking at the schematic-
The Operator Presence Relay controls the ground circuit to the clutch.
It is powered by the seat switch.
Those are 2 more potential trouble spots.
What I would do-
Unplug & plug all the associated connectors of the PTO circuit a couple times to "clean" the contacts.

I'd take an OHM reading of the clutch cold & when it's hot.
When the problem occurs try this for an OPR check-
Engine not running, but Key ON & PTO switch ON-
manipulate the seat switch to HEAR if the OPR is clicking.
You could expand this test and hook an ohm eter to the ground of the PTO plug and chassis ground. Manipulate the seat switch again and see if "ground is being completed in the "occupied" position of the seat switch.

Check your clutch and see if the air gap is adjustable-
Use this guide-
http://www.warnernet.com/pdf/819-0458_P-1097-6.pdf

When a clutch begins to act this way, it usually indicates that the clutch has worn some and the standing air gap (between clutch stator plate and clutch rotor plate) has increased wider than the electric coil is able to draw the clutch parts into engagement from.
The problem is aggravated by the fact that it requires more "effort" to draw the clutch into engagement, than to keep it engaged. The reason it will not engage after being engaged a while is due to all parts having gotten hot and expanded, thus making the already too wide gap............even wider, plus the fact that a hot clutch coil is less able to create a strong magnetic field (than when it is cool).
Adjusting the air gap to .012" in some cases is all that is needed to restore operational performance.
However, the detail you cite about that unidentified piece of rubber................might indicate that the clutch is suffering some other problems too.
Accept the fact that PTO switches are not everlasting components also. The duty that the switch does is fairly demanding and therefore it is not unheard of for them to fail, especially when around 11 years old and already exposed to carrying a heavier load than normal. I'm not saying your PTO switch is causing your problem..........I'm saying that the switch may be right on the cusp of failure due to age and use.
Regarding any potential changes in wiring, don't even think about it....unless you are a highly qualified automotive wiring technician. "Hot wiring" a PTO clutch is only used to determine whether (or not) a clutch is actually working. You never want to operate a PTO clutch in a "hot wired" condition.
Since it seems that you are on the way to tinkering with this clutch, beware that there is an "anti-rotation" bracket or other means of holding the clutch assembly from turning................make certain you recognize that feature and get it mated back correctly when installing the clutch..........otherwise the clutch is gonna spin as an assembly and rip out all the clutch wiring in the process.
You can find the official Warner clutch service and troubleshooting guide online.....free in PDF.

Thanks for the advice I got here.

First, note that once you remove the clutch, you can only move the tractor by pushing and pulling unless you reinstall the whole thing since the clutch assembly holds on the drive pulley for the powertrain.

I pulled the clutch today without any problems. It takes a big wrench to hold the end of the clutch assembly in place while turning the bolt that holds it to the driveshaft. There is a key / key way for both the drive{{gwi:807}} pulley assembly to the drive shaft and the clutch assembly to the drive pulley assembly. Made note of the slot on the pulley that fits in the retaining pin on the frame to prevent the clutch from spinning.

Once off, I discovered the bearing assembly on the top of the clutch was minus 6 - 8 ball bearings and the seal for the race was shredded. That was what I had seen sticking up earlier. I think the clutch would heat up as it ran because of the bad bearings and eventually kick out.

The specific model clutch is a Warner Electric Mag Stop MSS-60-LC 5217-2. I found a replacement on line from DB Electric in Kingsport, TN (http://www.dbelectrical.com/p-7171-new-electric-pto-clutch-ariens-lawn-garden-tractors.aspx) for $93.90 plus $7.95 shipping and it has a 1 yr. warranty. Beats Sears partsdirect which is about twice as much. Hope it goes on as easily as it came apart.

This post was edited by TopDawg69 on Thu, Jul 25, 13 at 14:33

Pay particular attention to Warn's instructions for burnishing a new clutch.

http://www.warnernet.com/pdf/819-0458_P-1097-6.pdf

Thanks for the tip, I would not have known otherwise! Here are the instructions in case others visit this thread.

Burnishing Procedure for Electric
Clutch/Brake to be performed with mower
deck attached.
1. Run at 50% throttle.
2. Engage and disengage the clutch 5 times.
(10 seconds on/10 seconds off).
3. Increase to 75% throttle.
4. Engage and disengage the clutch 5 times.
(10 seconds on/10 seconds off).

I installed the new clutch and it seems to work fine. I assembled a series of photos and a short video along with instructions and posted it to YouTube at this link.

http://www.youtube.com/watch?v=KpZER2AVun0

Here is a link that might be useful: Craftsman electric clutch replacement

Make sure you got the clutch bolt tightened to spec. Can be very costly if it comes loose.

Guys - just want to say thanks for all the advice. I had this exact same problem on my Craftsman tractor and replaced my clutch for $93 shipped. Took 10 minutes to pop in the new one. Got it from DB Electric via Amazon - I got the part in one day with their free ground shipping.

I was never able to find a torque spec for that bolt, however. So I used 50 foot/pounds which seemed reasonable given the effort required to break the bolt in getting it out. Does anyone have a better number?