Do the straps break easily on the HANGTUFF Targets?

No. The strap is made of the same material as the target. Random hits on the target give you random hits on the strap, so the strap holds up about as well as the target itself. If deliberate attempts are made to "knock" the straps off, of course, it can be done - however, most shooters will concentrate on the "round", or "Bullseye" part of the target.