Am I doing long term damage by running with mild patellar tendonidis?

Probably not doing significant long-term damage, but you are risking short- to intermediate-term problems.

If you can run without pain, you should be fine. If you have pain, your body is telling you to slow down, ease up, or stop. Would you like to video or text chat with me?

It's ideal to treat tendinitis in the early stages.

Trying to exercise in a manner that may cause continued irritation of a tendon is not wise. Tendinitis may become tendonosis which implies a chronic degeneration of the tendon. Once it reaches thus stage, it's not easy to treat and recovery can be lengthy. So, seek treatment early and don't push through this pain at this point. Would you like to video or text chat with me?