We have cows in the 20's still producing. These are the heifers we want to retain. They just had a sale close to me where 2001 Angus cows were selling anywhere from $3750 and up without calves at their side. Their numbers were not spectacular. So, cows are producing longer if you give them a bit of grain and Rumensin to help utilize the feed that they are taking in. Mostly the older girls.
A thirteen year old cow doesn't alarm me at the age other than something else is going on. Unless she is very shy and is being pushed away by more aggressive cows. Does she have bad teeth? Something else is going on other than her age.
I do not get rid of any cow as long as she has a good calf and is in good condition.
I read where many people unload cows at 7 years of age, and some younger, but they still have many more calves to give if it is a good cow. If it is a cow giving low weight calves, then I am for selling her. Otherwise, she stays.
If you take care of your cows nutritionally, the older cows will be around to produce for a while.