How about the fuel cap vent hole? Plugged possibly?

If it's fuel related, I had one tractor where the gas line was cable-tied to the frame, by the factory. Over the years, the fuel line had pretty much closed from the clamping effect of the cable tie. Remove the fuel line just before the pump or carb and check for a good volume of fuel. Safely empty at least a quart or two.

If it was a sheared flywheel key, you would not get 10 minutes run time before stalling.
If you are concerned that some of your close encounters with rocks might have damaged the flywheel key, rest easy. Whenever the blades are "belt driven", sudden stops of the blades don't result an instantaneous stopping of the crankshaft. The belt (or belts) slip and stretch and that absorbs enough inertia to protect the key.
Everything you described (disengage PTO, close throttle) points to a clogged (or partly clogged) fuel tank cap vent.

Thanks for the quick responses!

I have good fuel volume as I drained the fuel tank to work on the carb. I did it a couple times from both ends of the filter just to be sure. But, the lines are a bit cracked so it might be smart to replace them now.

That's great news about the key....I was worried about damaging the crank with all these stone hits, nice to know I have a little wiggle room - but I need to be more careful.

The gas cap vent. Interesting....I did read about that in another post and tried mowing with the gas cap really loose but it still tried to stall. It does have gunk on the top so I'll blow the cap out tonight and give it another try.

It's been raining here all day so I probably won't try mowing tonight, but as soon as it dries up I'll report back.

Thanks again for taking the time to help me out.

How old and in what condition is the battery? Are you charging 13.5V to 14.5 V ? Do you have an electric clutch?

Maybe an overheated coil???

Baymee, the battery is about 4 years old. I will put a voltmeter on it next time I start it and report back.

From what I understand about the coil and how it operates I'm confused. If mowing for 10 minutes caused the coil to overheat and stop sending a charge to the plug, why would disengaging the blades and lowering the throttle cause the engine to return to idle? Could the coil cool off that quickly?

I read many other posts that pointed to a bad coil but I would expect an overheated coil to completely stall the engine but when cooled down allow the engine to restart. If I'm way off base please let me know so I can better understand.

It's an MTD Yard Machines. I don't think it has a clutch - to engage the PTO you pull a handle down, it feels like it's mechanically engaged?

All true. I guess I'm clueless

Everything keeps pointing to a bad bearing somewhere, I just assumed a bad bearing would squeal and be really loud. Has anyone else dealt with a bad bearing and how did you know?

I'm going to take a closer look at the idler pulley's on both the tractor and deck tonight and see if anything looks odd.

Any chance a bad bearing would work normally for 5-10 minutes and seize up?

***"Everything keeps pointing to a bad bearing somewhere"***
I don't know what makes you "read that" into this problem.

***"Any chance a bad bearing would work normally for 5-10 minutes and seize up?"***
No, not in the sense that your problem has been recurring at regular intervals.
If a bearing were to "seize up", it would probably be accompanied by a belt squealing and you would see smoke from the belt. And you would likely only get maybe one or two repeat performances of bearing lock before the component (that the bearing is in) either flew to pieces, or simply locked up........never to turn again.
Go ahead and inspect your bearings as you wish, it's never a bad idea to know the condition of things, but don't expect your stalling to be related to that system of parts.

Resolution - my issue turned out to be a bad magneto. I did some more research and found that the issue happened when the engine warmed up. $40 dollars and 10 minutes later she was running like a champ. Thanks to everyone who took the time to offer help and advice.