Air carrier pilot reported that during a go around due to descending below the glideslope; the Autothrust disengaged.

Narrative

The aircraft was not adequately slowing with gear down and flaps 3 inside the FAF. AP (Autopilot) and A/THR (Autothrust) were engaged. The PF intervened with speed brakes and the aircraft responded with significant negative VSI. The aircraft descended below the g/s beam and the PF executed a go around. We assess the lowest altitude reached to be approximately 600-700' AGL. The A/THR disengaged without pilot input during climb on the go around. We believe there may have been unfavorable winds aloft that contributed to the inability to slow to final app speed. We don't believe slowing earlier would have helped for that reason. ATC assigned 170 to the FAF and we complied with that instruction. Unfortunately we did not recall what the engine power settings were when commanding the slow down. The disconnection of A/THR with out commanding it was concerning and we could not figure that out.