almost, but not quite, too late to do something, at the last minute
The Billabong had been saved at the eleventh hour. BNCI
Although the outlook may seem bleak, a constructive approach towards consultation might result in hitherto unconsidered options coming to light which could enable your job to be saved at the eleventh hour. BNCI
She had come to the Centre in the depths of despair, weeping, gnashing her teeth and venting her hatred upon the doctors who had told her, at the eleventh hour that she had cancer and nothing could be done. BNCI