I have the Droid Incredible and I use iheartradio and tunein radio apps to listen to Rush. They are both free in the Android market and work great. I tried to go to Rush’s site but I think the archive is for members only. Is there a non members-only link I could try out for you?
I also wrote a bash script to rip a radio stream and convert it to an mp3. I can then copy it to my phone and listen to it at my convenience. I may convert it to an app one day but there may already be apps that can do that... I haven’t checked.
I am a member. I can listen on my home computer and on my work computer (after hours). I can even sign into my account on Rush’s site on my Droid phone, but when I click on one of the archived shows, nada.