What kind of tow rope were you using? Ordinarily I'd recommend a beefy tow strap rated much higher than than you think you'll ever need. The shock forces involved in towing a vehicle can be surprisingly strong. I think my strap is rated somewhere around 20,000lbs. I'd also stay away from the straps with tow hooks.
The tow hooks can become very dangerouse if they slip off because the tow strap will slingshot the hook at one of the two vehicles.

The tow hooks can become very dangerouse if they slip off because the tow strap will slingshot the hook.

Also I will have to respectfully disagree with the previous post about using a ball hitch as an attachment point. I have heard many horror stories about these balls being sling shotted just like the tow hooks. You would be better off removing the ball, inserting the looped end of the strap into the reciever hitch, then passing the pin through the eye of the loop inside the hitch (as if you were securing your tow ball)
In addition the tow straps that come with tow hooks attached to them tend to be weaker, lighter, and generally of poor construction. However, an Acura probably will not have tow points designed for a hookless strap, so you may want to buy a few D-rings to go with it. These can generally be found at offroad supply shops, auto parts stores, home depots, Gi Joes, etc.

How far did you tow the vehicle? Maybe the strap was damaged from being drug on the ground? Could maybe try putting a sleve over the strap.