Mom's shoes keep disappearing. Do I just have to keep buying new?

Have seen residents hide their belongings very well, check everywhere in the room, every nook. Ensure Unit Manager is informed. Care staff should be told so they check the bin before emptying as sometimes residents put things in the bin.

If you buy her another pair of shoes if they are sneakers buy the brightest pair you can find. Swap out the laces with some of the neon colored laces. This way if you happen to see them on another resident you can easily claim them. (If you can't find bright colored ones get some fabric paint and paint a neon stripe on the ones you do get.)
You could get some of the "tiles" that are used on luggage so that it can be tracked. But if they do end up in the trash it will be a difficult item to get back.
Same with slippers, get the brightest colored ones you can find.
Your other option would be to look for shoes at resale stores so that if they do go missing you probably have not spent more than a few dollars.

If she has a roommate look in her closet. Look under the beds.

Make sure you have a good marker and put her name inside of the shoe. Make a mark or place a patch somewhere on the outside where u can recognize them when u see someone else wearing them. Take a picture of the sneakers. Take a picture of everything she owns. It helps when the aides go looking for the item. Take picture of eye glasses and hearing aides.