SSH with Apple Airport Extreme Base Station

When I connect to an SSH account (for privacy) to download something, after a period of time (not sure how long but I'd guess under 2 hours) my internet connection goes out. I think I've narrowed this problem down to the AEBS because first of all, all the lights on my cable modem continue to blink like they're supposed to if I have an internet connection, and second if I connect to the SSH account through just my cable modem (by taking the AEBS completely out of the loop) my connection never goes down. EVERYTIME I put the AEBS back into the mix (while using SSH) I get this problem. Anyone heard of this? Does anyone have a solution?