Absolutely been having the same problem using Firefox for quite some time now.
1. Sign in
2. Hover cursor over SEARCH or click on it. Box appears to type in search data
3. Move down to type something in. Box immediately disappears before you have a chance to type anything.
4. Start typing a post (as I am doing now). Box stays put to do a search
5. Open another window and enter the forum (signed in). Box stays put - no problem
6. #4 and #5 are how I have been tricking the search box into behaving.