is the spindles that attach to pulley and then to blades. loose? allowing pulley to move up and down?
have you taken off the "shields" while mowing. to make sure you are not cutting to tall of grass, and causing blades to jam up completely. causing belt to just melt / heat up around the pulley that the blade is stuck?
if you have the belt shields on. did you install them correctly? some shields will wobble/ bounce / vibrate some. possibly snagging the belt. i have had problems with shields over the years. were vibration of mower deck alone has sheared some bolts that hold the belt shields on. and before bolts / pins completely sheared, the shield was allowed to move enough to tear up the belt.
hitting a stump should not cause a belt to tear up. the belt should slip around pulley. and most likely damage a blade. vs tearing up belt. at least that is my experience.
on other hand with others, there are different grades of belts. the allis chalmers CA with belly mower. using very long belt. that costs close to $100 bucks.
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other thought, do not use any sort of "belt grip" spray stuff or like. on the belt or pulleys. the stuff may cause more belt slipping pending on what the belt is made from. more slipping = belt heats up quickly. and just melts / tears up. also more heat can cause more stretching. perhaps enough to cause enough wobble in belt. to allow belt to snag something and break.
double check your 3pt hitch arms and linkages. and as your mowing, make sure the deck is not rising up and then slamming down into the ground. (could be front of deck, could be rear of deck rising and slamming into the ground) the slamming into the ground may be causing belt to slid off of tension pulley and in a heart beat, belt gets messed up.
on new belt, give the belt a break in period. as to allow the belt to stretch some. and wear some, to your pulley groves. perhaps there is enough friction going on, that is causing new belt to over heat. to point it goes over belt ability to handle the heat and then breaks. other words do not get on mower, and go at it for a few hours. get off tractor and check belt every 15 minutes. and see how it is doing. for the first 2 to 6 hours. ya you should not have to do that. but... *shrugs*