Nobody is responsible as such. The council can resolve to allow a councillor to go past the six month period and remain in office if his or her personal circumstances are viewed sympathetically , recovery from a stroke, operation etc. But there is no obligation for the clerk or council to remind a councillor that the six month deadline is imminent etc even if the PC is quorate. That said, a good clerk would make the council aware of an imminent six month deadline and suggest that those getting close to it could be sent a reminder.