Using the Evernote Mac desktop app 10.111.2, I can duplicate the behavior you reported. To search again, as you reported, you can close the search box, then use ⌘F again. Alternatively, you could click in the search box and edit what you're searching for.
⇧⌘F will open the search and replace within note, as I understand is the way you'd like this to work. However, this only works one time. After that, you're in the same boat of needing to close/reopen the search box or edit it.