Weird Safari Issue...

Here's a really bizarre behavior Safari exhibits with me:

I use Safari as my main browser, and I use Firefox for some work things that Safari either doesn't have full compatibility with, or is very slow in loading and displaying. (They are corporate portals I use for work.) Whenever I access one of those sites securely from Firefox, Safari stops responding to page reloads, calling up new pages, etc. The application itself works fine, but Safari seems to "lose" its connection to the WAN. So I have to quit Firefox, and re-launch Safari.

I have not had time to test the various permutations of this scenario, but has anyone else experienced similar behavior from Safari - where it will seemingly lose its ability to load pages?