Hagar, I've not had any problems. They're heavy duty.
When I was trailering and putting the bikes on back of the pick up a lot, I'd buy a new set of tie down straps every year, and write the date down on them. Cheap insurance. Ive seen lots of ebay ads over the years for damaged, used bikes that had fallen over, supposedly by torn or broken tie down.
If you don't have some sort of wheel chock, be sure and strap down the front tire. Just because the top of the bike can't go one way or another, doesn't necessarily mean the bottom won't go anywhere. The result is the same.