This is a very well known phenomenon.
There are pages and pages of rage on the rift forums about it. http://forums.riftgame.com/showthread.php?81668-Your-external-IP-address-has-changed-since-you-Authenticated.
There are some workarounds but not very good ones.
What is happening is that the login server uses different services than the actual game and some routers or 3G connections will route these differently so that Rift thinks you are logging from a different IP to the one you are trying to play from. It may be possible to use a proxy to unify this but I'm not sure that is a universal solution.
Their attitude seems to be that everything is working as intended and no fix required.
I have found that if you keep trying you do get in although it may kick you if you return to the character select. I'm in a hotel now and with the game crashing whenever I port to Meridian I'm not sure its worth going through all this. I'll probably find out this evening.
Edit: Added link Edited, Jul 6th 2011 2:03am by Cobra101