Recently I had to wipe and re-enroll a couple of these old devices and they will not activate. Wiping via AC 2.7 or via on-screen GUI gives the same results, full functionality but does not activate. The big problem is that you can not install profiles using AC on devices that are not activated. There's an Activate button in AC but that results in an error. My 3rd gen and 4th gens devices activate okay, and 4th gen and 4K devices work even better with DEP (thanks Apple).
I have contacted Apple support and they do not have an answer. My hunch is they have quietly cut off activation on these 6 year old devices. It does not cause issues for unmanaged use but prevents enrolment in MDM or installing other profiles.
Is anyone else having this issue? Or is it time to finally throw these hockey pucks in the bin?
I'm honestly amazed that you have a 2nd generation AppleTV that is functional. Bare in mind that in terms of hardware, these things are equivalent to an iPhone 4.
I would toss them and never look back.