I started experiencing this bug very suddenly. But a few events lead up to it for me so I figure I should share. The menu was working fine, and it this all happened after I spent several hours building a hotel complex. I finished it, and traveled to my home lot via the world selection menu.
Things went weird here. When I selected my home plot in Chestnut Ridge, my main character, Lance, was showing that his location was "Secret" even though I just left him at my new rental plot in NewCrest. I selected another household member so I could load into my plot, then recall Lance to it. At this point, the game locked up. It sat in the loading screen for 10 minutes before I gave up and force quit. No matter what I did, every time I tried to load into my home plot, the game locked up. The only way I was able to get around this was to go into a totally separate household that knew Lance, and invite him over to visit so he would spawn in. Only then could I get back into my main home plot again and recall him to that lot. No issues with that since.
It was after that incident that my owned businesses menu stopped working. Neither the rental plot, nor my vet clinic would show up anymore. I sold and repurchased both businesses, and this did not fix the issue. That's when I looked this post up. I tried the trick where you go into build mode and back out, and it only worked for my Vet clinic. My rentals still refuse to show up in the menu. The game acknowledges that I own both properties, as I can go to them and enter build mode. But they refuse to show in the business menu.