Does Suvarnabhumi Airport in Bangkok handle round-trip visas 24 hours a day? . . . . urgent

Yes, the immigration office for re-entry visas is available 24 hours a day, but you have to check in at the airline counter to enter that area, and the counters opened by airlines in advance are generally not much ahead of time. If there are more people with re-entry visas, then you will keep the whole flight waiting for you. It is best to apply for a re-entry visa at the urban immigration office.