A guy put 25 pounds of books, a 100 fl. oz. case of laundry detergent, and a 2.5 gallon water jug on a sling suspended only by a Wii strap and it held just fine. After he added the jug, the contraption flipped and smacked him in the face. Wii strap still intact.
What finally did the strap in was him holding the Wiimote in one hand and the strap in the other, pulling and heaving so hard that he started to shake. This process finally made the strap break off.
Conclusion: regular usage shouldn't break the strap. Advice: don't swing the Wiimote around like goddamn David of Goliath fame.
Oh Snap! [Nintendojo]