Hi,
Open a Finder window.
Use the View Menu > Show View option and select the Modified column.
Again in the same Menu select "Show Path bar"
When you have done these the route to the folder of file at the top of the current folder will show across the bottom of the window.
The window, if you are using Cover Flow for instance, will also show a Column lists as Modified.
Now use the Go Menu in the Finder whilst holding down the ALT key
Select the Library.
Navigate to Preferences
Find the com.apple ichat.plist and highlight.
1) Does the Modified column change if you change any setting in the General Section of the Messages preferences ?
It should show a time rather than Date if it is being refreshed on changes.
Now with the item highlight do a Get Info (CMD + i keys together)
2) Does this show your Name in the list (it will be your Short name) ?
3) If you highlight your Name and then use the cogwheel type icon below the names list does this then read "make your Name (Me) the owner" ?
If it is greyed out as if already done then you Own it.
4) Do you have Read and Write permissions to the file itself ?

I.e. in this Pic I am the owner and I have Read And Write permissions for it.
Now in the Finder Window right click the Preferences Folder itself
Select Get Info and check your Own and have Read and Write permission to the Folder.
Repeat for the Library item as well.
Pic showing me right clicking the Library in the Path Bar.

I will let you post back with that info first.
It may not be the end of checking as in Mavericks the app uses a Sandboxed path to write to the .plist and the issue may be with that.

8:38 pm Friday; January 3, 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