Mechanic misdiagnosed car?

To start off, I have a 2007 Ford Focus. Approximately 2 weeks ago I took the car into my mechanic because the steering wheel was making loud noises when I made turns. The mechanic charged me a diagnostic fee of $60 (which went toward the cost of fixing the car).

After diagnosing it, he said that the power steering pump needed to be replaced. He quoted me $380, and I paid. About a week later, the issue occurred again. I took the car back in, and he replaced the power steering pump again. The mechanic told me that pump they put in wasn't working, and was covered under warranty.

I wasn't too upset until I was told that if the pump has the same issue again, it's going to be approximately $700-$1000 to fix the vehicle. I can't remember exactly what the issue was, but I'm confused because shouldn't that have been revealed when the diagnosis was done?

I feel like they're giving me the run around

Read the paperwork you signed. I bet you have very limited rights.

Find a new mechanic. Charging you money just to tell you what's wrong with it, without actually fixing anything, is goofy. The price for the initial repair was too much, and why would it be double later on? On top of all that, they obviously mis-diagnosed your problem (which is ironic, since you paid for it).

It seems like he got a cheap autozone or oriellys part, replaced it twice and now has to get an original one from the dealer, it happens to more often then not.

You don't even know enough to tell us the year, make, and model of the vehicle or where you took it for repairs. How do you expect us to guess what the problem is?

They may NOT have misdiagnosed anything. It is possible you had more than 1 problem, and the power steering pump masked the other issue.
Unless you can find a mechanic willing to state that isn't the case, you have the right to keep paying or to not have them keep working.

You never had a bad pump, you had a leaking steering rack and they finally figured it out.

Hmm. Just a guess. Your fluid was low they said they put in a new pump but didn't just cleaned up the old one and fixed the leak or though they fixed the leak and it leaked anyways and your back again for common low fluid moans.