Well, let’s assume that it isn’t the mac screwing up. The only thing I can think of to recommend is buying an Airport Express and plugging it closer to your Mac Mini, the only problem is, you need to run an ethernet cord to the Airport Express. I recommend an Express because it is much, much, easier to set up on your mac then something else. However, I think it might be the Mac that isn’t working correctly. How far away is the mini from the router and how many walls\ceilings does the signal have to pass through?