Hi,
Can you explain which windows you have open in Messages and which of those are indicating that you were Off Line.
Messages with AIM and Jabber accounts wand displaying those Buddy lists will make the Status or yourself "Idle" after 10 minutes (the default idle time)
Then depending on your Filter settings for Displaying your Buddy Lists (Availability being one) AND how many AIM Account you might have logged in they will then bounce up your List turning from Amber (Idle) to Green (Available)
I have 5 AIM valid Screen Names logged in.
I display each in separate Buddy Lists.
On Buddy list has the other 4 as Buddies.
They all can go Amber if I walk away from the computer (If even have th Screen Not to Sleep as well).
Being Idle is not being Off line.
8:56 pm Thursday; July 24, 2014
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