I agree with Simon. I think it is an obnoxious and random Apple server problem.
Most of the time, handoff works fine. There are (what appear to be random) moments where there is a significant delay or it doesn't occur at all. And when it doesn't work, (which doesn't happen often) I go through the process of signing out of iMessage, FaceTime, and iCloud on all devices, sign back in, and everything works as it should.
Yeah normally that's the case... but with this bug it's not. The iMac doesn't even show up to the others. It's like the iMessage servers are completely sandboxing the computer. The weirdest thing is if I send an iMessage to someone, it actually says "Delivered" which is so bizarre, because the message never gets delivered.