I agree with a lot of the sentiments expressed here, but there's something I'd like to add.
The auction house (at least in my experience) seems to favor people with a lot of time on their hands (in addition to a lot of pixcoins). This seems to manifest as either: 1) an auction ends when you're not around (ex. sleeping), and since people like to bid at the very end of auctions, you can't even begin a bidding war for that item; or 2) you simply don't have the time to carry out an extended bidding war.

As a college student, I really do not have the time to be on pixpet constantly just to check the auctions I've bid on to make sure that I win that item in the end. I absolutely have the pixcoins to do it, but I just don't have the time.

In regards to scenario 1, this happened a lot when I was a new player just trying to get a second plant pot or a second pixpet. In addition to not having much pixcoins in the first place, many of the auctions ended when I wasn't playing. This can probably be combined with the fact that there isn't much reason to stay on the site for long periods of time (especially when you're new and there really isn't much to do but wait around).

Scenario 2 is more of a recent problem for me since I almost never use the auction house for buying things anymore (due to scenario 1 happening to me so often). The most relevant example I can give is trying to get one colocrow egg. I almost gave up the small bidding war for that egg just because I had to get ready for class soon! It worked out for me in the end, but it really highlights the fact that some people may just stop bidding because they no longer have the time, rather than being worn out by the other player (not that either of these situations are ideal).

I personally don't have any new suggestions for a solution to this. As I've said, I avoid the auction house as much as possible just because I dislike the system so much. I'm not very competitive, so I dislike bidding wars and having to bid on an item more than once. It seems ridiculous to me that in order to enjoy this site to any capacity that I have to avoid such a big part of it. There are items I will probably never obtain even once just because I won't use the auction house to get them.