The special is awarded via a switch closing on the H relay, when the domino 'Advance' Unit is at the 14th position (i.e., maxed out). The left/right rollover switches should activate the H relay, and if the Advance Unit is maxed (so Special is lit), the switch closing on H should award the replay when the score motor runs and a switch at motor 2C closes.
Since the kickout holes are working to award the replays, that means everything else on that path is working, so it's only the switch on H, or H not activating as the prime suspects.