Hi,
If the Internet Speeds don't drop off and there have been no major changes to the Internet Service the issue is either outside the remit and control of the ISPs (i.e. the internet backbone for example) or something has changed in the Messages App or something within the OS that is effecting A/V chats.
The Log you posted earlier and others I have seen don't suggest the app itself has changed.
Apple did have at one time some auto-responding AIM valid IDs but these have not been available for years.
This make it difficult to any staged testing.
Effectively these computers appeared to have their own IP on the Internet which lessens the issue of going through a router at both ends so a test is only a partial one of a router at each end but it did used to at least prove your end was set up correctly.
The only other options involve tweaking the Login options (not using SSL, trying an older server name and so on).
However this will have little effect on the Peer-to-Peer connections in Messages when doing A/V chats.
There is an option in th Privacy tab settings that allows your to Relay through AIM (AOL) which it might pay to toggle it opposite to what you have currently (mine is set to relay so I would have to disable this settings myself).
I have no other suggestions at the moment.
It looks like we will have to wait.
8:04 pm Tuesday; July 21, 2015
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
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