MD-11 pilot reported wind gusts and a loss of lift at 30 feet resulted in a hard landing. Aircraft was taken out of service for an inspection.

Narrative

Flight 4 hours delayed to ZZZ due to mechanical and tail swap in ZZZ1. I was pilot monitoring (PM). First Officer (FO) as pilot flying (PF). Arrival into ZZZ Runway XXRCaptain as PM; FO as PF. Arrival into ZZZ ILSXXR. ATIS winds 310/15G25 with LLWS advisory in effect. Winds approximately 310/16G22 from Tower ATC landing clearance. I remember thinking 6-7 kt gust and ATS consideration for approach speed. FO did well controlling speed on final and maintained stabilized approach criteria with momentary wind gusts and proper corrections for speed and pitch. Autopilot disconnected at approximately 500ft and pitch and aim point stable. Approaching 50Ft PF adjusted power and maintained landing zone; at 30Ft it felt like there was a drop off in lift. Cadence from 50 to touchdown was normal. The aircraft bounced; I called go around; aircraft settled to runway I looked at throttles to take the aircraft and initiate Go Around and saw PFs hands on reversers; he held the nose and asked are you sure and I told him to hold the nose; continue landing; I took the aircraft and completed the landing rollout. Logbook entry for firm landing and debrief with mechanic. LR showed 1.8 and post briefing from mechanic agreed with that. Aircraft subsequently removed from service for inspection. The winds were within the crosswind limits and we briefed the threats of the wind conditions with the potential for wind shear. The PF made positive inputs throughout final approach. I believe our long duty night and early onset of fatigue contributed to delayed reactions and responses. I may have missed an earlier cue and the FO may have processed my go around call differently. We discussed any initiation of reverse thrust for staying on the landing vs executing Go Around. Will maintain constant vigilance and continue to fight to recognize the final few seconds for aircraft cues and performance.