Hi! This is an excellent question and I want to add my .02$ worth.
As a Certified Crane Operator (the BIG hydraulic cranes you see at job sites as well as the BIG and small overhead cranes used inside manufacturing facilities) and a long time OTR flatbed truck driver I have a bit of background on safety equipment such as straps and chains.
For cargo straps there is a rule that anytime the strap is cut more than a third of it's width that it is deemed out of service. I will follow this up by saying that you should NEVER use securement straps for recovery. It is NOT what they are designed to do and there is no way to judge what is safe or unsafe when you use them outside of their specific design.
On lift and rigging straps used with cranes there is a red thread sewn in the strap. Once this red thread is seen the strap is deemed out of service. RED IS DEAD!!! These are more the type of straps that we use in recovery because they are designed to LIFT and pull rather than HOLD DOWN like securement straps.
While these are good guides they do not answer your question. Quite frankly you won't get a positive answer in a forum such as this. The only way you can get a good positive answer is to contact the manufacturer of the strap and ask them when to take the strap out of service.
When in doubt you should always err on the side of safety and replace the strap. As 762X39 said "Straps are cheap, life is precious."
EMT-I/99 I do rescue
2001 Jeep XJ 2.5 inch lift, 31x10.50 BFG A/T's.
Ebay Winch Bumper, IRO steering and track bar, RE LCA's...
Nifty wiring harness for extra stuff, Red top, more stuff...
I get really bored sitting still. 2,000,000 miles in a tractor trailer across the USA is not enough. I want more, but this time without a load behind me.