Just a thought, Da Bear. And believe me, I am not judging your operating practices, because that sounds like something I would do.
But depending on the circumstances, I can see how pushing on a tree like that could cause excessive strain on the front axle. Sure, it should be tough enough to allow for some slippage to occur, even while carrying weight with the FEL. But, if you were steadily applying upward pressure on the tree while pushing it with the FEL, the dynamics of how the tractor is built would cause a huge amount of pressure to be put on the front axle. Think about it-
When lifting a heavy load with the FEL, almost the entire weight of the load is carried on the front axle. When the load is heavy enough to lift the rear of the tractor, the front axle becomes a fulcrum point and supports the entire weight of the load and the tractor. That's a lot of weight, which equates to a lot of downforce on the front tires.
Say there was a scenario in which you were pushing on the tree with the FEL, applying upward pressure trying to uproot the tree, maybe enough pressure to cause the rear of your tractor to become light. That would mean the front axle has become the fulcrum point. Now if you tried to push the tree while in this scenario, the added downforce on the front tires could create significant strain on the driveline components, especially if the tires were slipping and churning for traction.
Couple of years ago a friend of mine had a front axle shaft fail on his Kubota M5660 while doing something similar. I'm not saying that's your issue, or even that the above scenario is what caused your issue. Like I said, just a thought on possible causes.
Either way, sorry to hear that you're dealing with that. Hopefully it isn't much of a hassle for you warranty and repair-wise.