I'd say it's more likely that he was excluded because he was dead, unless there's a precedent for posthumous honors.
Regardless of what caused his exclusion, though, what is obvious is that the Kennedy Center feels no obligation to include all members of a band, past and/or present.
I daresay the decision regarding which Eagles would be honored was the Kennedy Center's, but doubtless there will be those who immediately condemn Glenn Frey and Don Henley for it.