It had been widely believed that at yesterday's meeting of Labour members of the Welsh Assembly, Mr Davies would be forced to resign as chairman of the influential economic development committee.
But after addressing the group he emerged Houdini-like to declare: "I won't be resigning." After the meeting fellow Assembly members issued a statement saying: "Mr Davies has agreed to reflect on the views of his colleagues."
Labour members were meeting for the second time in 24 hours, underlining concerns raised after Mr Davies' recent admissions that he was bisexual, given to living dangerously and was undergoing treatment for a psychiatric condition. He was not at Tuesday's meeting - he was in London giving a bravura performance at a devolution conference organised by the parliamentary journal The House.
Yesterday's event got off to a shaky start after John Marek, MP and Welsh Assembly member for Wrexham, walked out after 10 minutes, declaring that he would not take part in a meeting that was "intent on getting Mr Davies".
Dr Marek said: "[Mr Davies] is clearly the person best equipped to chair this important committee. We cannot afford to lose someone of his calibre."
Labour alone cannot force Mr Davies to resign the chairmanship. The party holds only 28 of the 60 seats and needs the support of opposition parties. Plaid Cymru, which has 17 members, supports Mr Davies because of his success in achieving devolution. The six Liberal Democrats refuse to criticise him.
The mathematics leaves the nine-strong Tory group in a powerful position. But the emollient nature of the Assembly's procedures - members frequently address one another by their first names - may count in Mr Davies' favour. The Cardiff style of cuddly politics means that tea and sympathy are more likely to be dished out than marching orders.