Thank you for your review.
This should not happen, the selection should stick and persist after restarts, etc.. Does this happen after a browser restart or just after some time? Do you have some specific about:config flags set that could cause this? Feel free to create an issue on GitHub: https://github.com/Brawl345/Image-Reverse-Search-WebExtension/issues?q=is%3Aissue+is%3Aopen+sort%3Aupdated-desc