I think I know what you're saying, when someone selects an option it causes the entire page to reload to show the new results and the option they had selected to get those results is lost correct?
I don't think you'll like the answer on how to do what you want, it involves using cookies.
Personally I needed a much more modern member search along with radius search capability so I built one from scratch using ajax so that each time a filter is changed it auto updates the results without refreshing the page.
I'm working on making it a component that I can distribute to other people but I need to finish up the admin controls to set your fields you want as search filters. I know there are a lot of people out there that really want this type of component so I'm going to try and get something ready to distribute as soon as possible but I don't have a lot of extra free time at the moment. The good news is it's almost ready, I have the radius databases packed and set so you can select what countries you want to install by just pushing a button in the admin control and have the basic framework setup for selecting your fields, I just basically need to finish up tweaking the code to display the filters accordingly.
I'll post something on Joomlapolis when I do get it ready and will post it in the jed so if it's something you want just keep an eye out for it over the next couple of weeks.