I can repro this on Firefox for Mac. I’m guessing it has to do with the order of the event when Enter is hit. When you use arrow keys to select a date, it updates just fine when pressing Enter. But in the search box, it closes the window, probably assuming that the same number is selected as prior.
I tried this on my personal site using the chat integration plugin (which also uses select-kit), and I was not able to reproduce. I had a chat with @joffreyjaffeux, and this has to do with the current implementation of select-kit getting confused comparing a string to a number. He’s working on a new version of select-kit, so this should be fixed when that gets rolled out.