I have been told by multiple people that they cannot do a wishlist search in my shop. Is there something special I need to do?
Chances are it's because the shop is too large and is timing out. It took awhile just to get the shop to load on my computer.
It's because your shop's too big. You can't search it regularly, either. It's not something you have or haven't done, shops are just horribly inefficient and need to be revamped at some point.

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Thanks people. At least now I know my digital life resembles my real life. Way too much stuff. At least here I don't have to worry about opening a closet and then getting buried by an avalanche.
Loving your look -- both of you. (Speiro, there is something about your eyes… absolutely mesmerizing!) :D
Thank you!
This has been an issue for a long time, and has been reported before here: [topic not found].
Based on posts made by in the suggestions forum, it sounds like the solution to this issue is going to involve shop item limits.
Outside of moving a large amount of items to another shop, there's not much you can do.
I'm going to go ahead and lock up this thread now. You're welcome to add your report to the thread I linked above, if you should so desire.