My doctor gave me permission to continue running. Further, he said that he recommended patients with worse conditions than I had to run, with no problems. If so, please, please, please let me know. The biggest risk of further retinal problems would be from trauma. The trauma of running is not very much on the eye.
Direct trauma is the bigger problem.
It is also possible that someone who had one retinal tear develop spontaneously can develop further tears. For this reason, you need to maintain continued followup with your ophthalmologist. I cannot say the risk from running is zero, but I do not think it is much at all. For more specific information about your own case, you would need to be examined. This information is for educational purposes only.