I don't think saving the results page is going to work, but you can do the search for your forum posts any time. If you want results which *don't* expire, although you'll get a list of each individual mention rather being broken down by thread, you can use google, and conduct the following search:
site:http://www.scirra.com/forum randomexile
If you bookmark the results page, google will just display the updated results every time you visit it.