Accept/Maybe/Decline Missing in Apple Mail

Open the Contacts app, select your own email address in the list of contacts. In the menu on top of the screen, go to "Card" -> "Make this my card". Reload calendar. Then it should work, you will get a notification popup with accept/decline buttons. (I just had the same problem, on a Mac running Yosemite) Source

I had the same issue. After searching forever to find a solution, I stumbled on an unrelated post that fixed the issue. Apparently, if your contact in the Contacts app doesn't have the same email address that you are trying to reply to/from, then you don't get those choices.

Basically, change your contact to be "me" in the Contacts application and they show up. Contacts>Card>Make this my card

on my iPhone:

The email address was already part of "my card". Still, I could not reply to ics-meetings copied to my calendar.

In General settings, Passwords & Accounts: make sure that "calendar" is also selected for the email account in question.

Initially, "calendar" was only selected for my iCloud account, but not all of my additional email accounts.