I apologize for this delayed reply to your gardening question and hope it is still helpful to you.
Such dog "traffic" is too much for any grass. If you can spread the foot traffic out a bit a tough grass such as Bermuda or Zoysia might recover from the damage. If they keep pounding the same spot such as along a fence line there is little you can do.
Thanks for the question. Best wishes for a wonderful gardening season. Please stop in again soon!
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