The baths suffered fire damage during the Nika riots in 532 as the rioters put the city to the torch. The great fire started at the praetorium of the prefects and extended into Region I (old Hagia Sophia, parts of the palace including Zeuxippos and as far as the Forum of Constantine).
Lydus (6th century), Malalas (6th century) and Theophanes (9th century) all provide the detail that especially the columns were damaged by the fire. [CHECK]
Procopius, as eyewitness (6th century), records that damaged/destroyed buildings such as the propylaea of the Palace, the Bronze Gate (Chalke) and the House of Ares, as well as the Baths of Zeuxippos and their colonaded stoas as far as the Forum of Constantine, were restored by Justinian afterwards (Buildings, 1.10.3).