HI,
If you mean that you happen to be "hidden" by the fact your Public IP address cannot be seen then you will have issues.
The AIM servers in particular need to know "where" you are in relation to the whole internet.
They will in fact Suspend AIM Accounts and even Apple ID that are Valid names if they suspect "Unusual Activity". Recently this has included trips abroad and using the Screen Names from somewhere else.
The AIM account and the iMessages account require and Always On connection (much more than a Browser or the Mail App uses).
Any time the servers cannot maintain the connection you will get dropped.
This is turn may lead to issues about signing back in again.
For Instance the AIM servers keep track of whether you are connected or not.
There is a .plist called com.apple.iChat.AIM.plist that is used in Messages as well as iChat that holds the apparent status of your App regarding it's AIM login.
When the two don't match you can get "refused".
As we know iMessages uses the Mac's own Serial Number to generate the Auth-Token then we can presume a similar state is used here.
9:49 PM Saturday; February 2, 2013
Please, if posting Logs, do not post any Log info after the line "Binary Images for iChat"
iMac 2.5Ghz 5i 2011 (Mountain Lion 10.8.2)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad
"Limit the Logs to the Bits above Binary Images." No, Seriously