A 759 addendum No.

A dire eagle does not have either Improved Grab or Improved Grapple. It will provoke attacks of opportunity when attempting to start a grapple, and if an AoO deals damage then the grapple attempt fails.

Should the dire eagle succeed in starting a grapple, it would be unable to move unless it succeeded on an opposed grapple check as a standard action. That allows moving at half speed. A dire eagle's average maneuverability requires moving at minimum half speed horizontally, so there would be no possibility of gaining altitude. The dire eagle would also be limited to its light load limit; flight with heavier loads is impossible. With STR 20, a dire eagle's light load limit is 266 lbs. (133 lbs. for STR 20, x2 for Large size). [The figure of 399 lbs. in Races of Stone is incorrect; an eagle is not quadrupedal (i.e., having 4 feet).]

If the dire eagle managed to move horizontally with its grappling foe over a drop (across a canyon, for instance), it could not simply drop the carried creature. Instead, it would have to win either an opposed grapple check (in place of an attack), or an Escape Artist check (as a standard action). Attempting either of these checks would prevent the dire eagle from making the standard action grapple check to move and maintain the minimum horizontal movement required to keep flying, so the dire eagle would always stall and fall, regardless of whether it succeeded in escaping from the grapple.