Why does the belt fall off cub cadet model xlt 1045?

This is a known problem caused by a design flaw.

It is caused by the tension pulley under the deck being too loose. The bolts may loosen themselves due to vibrations.

You should be able to tighten the bolts on the pulley yourself, that should resolve the problem for you. If the belt falls off again, just re-tighten the bolts again.

In 2007 there was also a recall for this exact product due to tension springs breaking. So the belt has not been the only problem with the product.