Is it possible to have a fixed URL that points to the results of a search on this forum?

The search url looks like:

"http://www.hydrogenaudio.org/forums/index.php?act=Search&CODE=show&searchid=405d2352331f8502c1b098c5ab72222d&search_in=posts&result_type=topics&highlite=%2B"

but this url doesn´t work after a few days.

The search form seems to use post data, so unless you make a script which sends data to the php script, I doubt there's a way to do what you want.