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.

The auction system is good for getting pixpet eggs to people. Though it could use some improvements, they need a simple confirmation popup to prevent lag and autofill from messing up your bids lost 3k that could have been prevented with a confirmation popup box.

I've only been on this site a short while but I have to throw my two cents in because the auction house has been nothing but bothersome for me. I struggle to get 100 pc+ items and eggs because players with more money than me love to come in and jack up the price to the point that prices I previously considered an economic deal become no longer worth it, and I struggle to get 1-10 pc cheap buys because other players love to get in tiresome +1 bidding wars with me or just grab the items while I'm asleep. This is to say nothing of how ludicrously long some bids are. I do not have nine days to sit around twiddling my thumbs waiting for one egg. It's a total lose-lose scenario and it makes me feel like the few bids I've won were total flukes.

In an ideal world, the usershop system would be a good counterbalance to this, however there's no easy way to search usershops. You pretty much have to either beg in the Discord or crawl the Dealer's Den sub forum hoping you find the specific plant, potion, or furniture you're looking for. I feel like the most elegant solution here is just making usershops more intuitive. Make them easier to search so I can actually get what I want instead of having to hope that maybe I stumble upon a well stocked user or that somebody else doesn't muscle me out in the auction house if someone miraculously puts up what I'm looking for.