Run flat tires and bent rims

I recently had a run flat tire go flat. I had it patched and it would hold air untill I got on the highway. I had the tire pumped up and put in a dunk tank, and they said they couldn’t find a leak anywhere, so I bought new tires. At highway speed the new tire loses air. The only thing I can think of is I have a bent rim. So my question is, if it is a bent rim why did it not leak in the dunk tank? What do I try next? Getting tired of spending money. Any suggestions would help.

Is the rim steel or alloy? I’m guessing alloy and I’m guessing it has a small crack or porous spot. Pump it up to 50 psi and try that dunk tank again…Make one yourself out of a kids play-pool. Few shops have a tank that can submerge the entire tire and wheel…

A wheel needs to have a smooth bead where the rim meets the tire. If you drove the car while the tire was flat, you may have caused some damage to the rim that is not visible and which will not even leak in all cases.
You can ask the mechanic to coat the bead with an adhesive to bond the tire to the wheel. If the tire doesn’t leak after that, in all temperatures, you are good. If it does, you need a new wheel.