Over the last 3 month, our 2005 Honda Odyssey has had a whining steering pump. Here's a bit of the background, from the day that it started until present.
One day in mid-October: Get a call from my other half, the car's making a loud noise. Diagnose it over the phone as the steering pump. Wife confirms puddle under the car. She'd only driven the car around the block. Call a mechanic ~5 miles away, they can get her in immediately.
$300 later, garage has replaced a line running from the reservoir down to ...somewhere. I regret not getting a specific part number at the time, and if potential answerers deem it important, I'll call up the shop and find out exactly what was replaced. Noise is gone.
....for about two days. I call up the garage: "it's back". They bring it in, clean it all up (to be sure that there is no leak in the future), bleed all of the air, and give it back to us. Noise is gone...
...for about two days. We noticed that it gradually returns, as air is making it back into the system. Again, we take it back to the shop. They confirm that everything is still nice and clean, ruling out a fluid leak. Fluid is still topped off. At this point, the shop tells me that I need to replace the pump, and that it was probably damaged during the initial failure.
Air is clearly entering the system, with no fluid leak at all. Apparently this can happen, but I'm reluctant to throw money at a pump that may not be the issue. In the back of my head, I'm wondering whether the new part that was installed has an issue. The garage is clearly baffled.
If they put a new pump in place, and the issue is still present, I might then be able to introduce the concept their initial part was faulty. They may, or may not accept this, and it may not be correct anyway. The shop is clearly not being malicious, but if they have no new ideas, is there a point in going back anyway?
Anxious to hear if anybody has an idea of what could be the actual issue.
EDIT 1
@DucatiKiller This seems to sing your problems song (youtube video link)
Sorry, I probably should have included info about that, on the question, too. After I took the car back to the shop the second time, I went googling and found that video. When I talked to the shop the third time, I specifically asked them about the O-ring. They seemed to already know what I was talking about, and said that it was "one of the first things that they looked for."