gitg is my favorite desktop tool to browse git repositories; I use it daily for code review @work.
Nearly since the beginning I've been limited by the search: There is no "find next" button, which means you can only search for the first commit that contains your search word.
Today I searched the bugtracker since I was about to submit that as a bug, and found the following issue:
Search bar only lets you find the topmost matching commit .
Interestingly, it shows how to find the second and third and fourth (and so on) commit: Press the down arrow key, and you'll jump to the next occurence!
You can also click on the magnifying glass in the search field and can select what to search: Subject, author, date or hash.