I use the Khazar's ability to bring back a Cry Wolf burned many turns
ago as a wraith.
Next turn, I my Wraith gets burned due to circumstances beyond my
control.
It's clear I could take the Khazar's action again, but can I also now
Compel the burned Cry Wolf card as a Cry Wolf, since it was an "ally"
that "burned since [my] last turn"?
No, since it is now a Cry Wolf ally minion, not Khazar's Diary Wraith ally minion.
That is, the card represented a different ally when it was burned than it (the
card) represents while it is in the ash heap.
For more on the effects of "representing" something else, see the thread
surrounding this:
http://groups.google.com/group/rec.games.trading-cards.jyhad/msg/15fb6ba56c2574c3