Hi,
If you are using an AIM or Jabber account then it should send Pics in line in the chats.
Having said that those of us that have been using Messages 8 in Yosemite and version 9.x in El Capitan have found this to more difficult.
The iMessages account has not seem prone to this drop out of functionality.
However if you run Little Snitch or similar "check and Monitor" firewall type apps it is possible to not allow a process that is needed by Messages to do this.
Example or Little Snitch.
There are two other processes that have File Transfer in the name that deal with AIM/Jabber sends and then the iMessages ones.
You should see pop ups like this to agree to allow
9:56 pm Saturday; April 30, 2016
iMac 2.5Ghz i5 2011 (El Capitan)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone and an iPad (2)