Hi,
There are many Jabber Servers.
With an App like Psi you can get linked to some that are "installed" in the app by default.
You can find names in lists.
Facebook run a Jabber Server (After your Enable Chat you get given a Chat ID variant of your Account ID)
Your firm obviously runs it's own one as well.
I have been using one called Jabber.Me.com which has recently stopped being On Line.
The com.apple.ichat.Jabber.plist would normally hold the accounts and the server info needed to log on to the Server.
If this had become corrupt then it will be recreated when you relaunch the app.
It will take note of the setting in the Messages > Preferences > Accounts > Server Settings for the accounts involved, such as whether it is supposed to be using SSL or not.
Jabber servers connections are either on port 5222 (Non SSL) or 5223 (with SSL).
Turning On and Off the SSL check box automatically changes the port.
In the case of Google Talk you can set the port to 443 and SSL and it will still connect.
The IMAgent item may reappear in the Activity Monitor again but with a new PID as it may restart itself before you can Restart the Computer.
Is this what you meant.
Can you confirm that you did try removing both Accounts as I suggested to the Original Poster ?
I would also suggest quitting the app in between that and re-adding them.
7:20 pm Sunday; January 12, 2014
iMac 2.5Ghz 5i 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