One of the things I do with RSS feeds is make sure that the links have the target="_blank" attribute. That forces the RSS link to open in a new window, leaving your site on the original window.
Some RSS feeds are hard wired with links that include the target="_blank", and some do not. To get around this I run a cron job (periodic job run on the server) that downloads the RSS feed to my server. Then I take the RSS, reformat it the way I want, include the target="_blank" if needed, etc. In general most RSS publishers like this cron approach since it puts the load on my server, not their server. Also, I don't have to rely on remote RSS servers being down. To minize faults associated with the RSS server being down, I do it a few times (usually at night) and throughout the day. That way if the RSS server was down I can pick it up later. The code that downloads the RSS to my server checks for blank returns so a dead RSS server won't write a big null file to my stored RSS feeds.
A bit complex maybe, but it works.