That really is not enough to go on.
For Instance if you both have AIM names (or AIM Valid names) then you could be set to Invisible and she would not see you as On Line.
As we are talking about iChat 6 here you could be doing the Same with an Yahoo Buddy List.
IF you are using Jabber (GoogleTalk, Facebook and others) then she may not have Accepted you as a Buddy when the Invite was sent.
iChat send this request once where other Jabber Apps send it repeatedly until the person Accepts or Denies.
If they don't Accept they can have Buddies that Appear to be Off Line (they probably have a Status Messages about "Waiting for Authorisation")
The only way to correct this in iChat is to delete the Screen Name form the Buddy List and Add it again when you know they can "answer" the Request to be a Buddy.
With AIM Accounts there are ways of setting things up in Preferences > Accounts > Security but you would not be able to see her on Line either.
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