text: He said it would be "hugely challenging" given current "strong anti-establishment thinking".
  No such poll is taking place, but his comments come after others warned of threats to devolution in Brexit's wake.
  In response, Plaid Cymru leader Leanne Wood said the EU result should not be read as a vote to "centralise" power.
  During the referendum campaign Labour, which leads the Welsh Government, and official opposition Plaid Cymru campaigned to stay in the European Union, while Mr Davies campaigned for Leave.
  Leave won in Wales, and since the June vote First Minister Carwyn Jones has called for any future Brexit deal to be put to Britain's devolved legislatures, saying he would set up an advisory group on the issue.
  Mr Davies said there was "no great warmth or affection" towards the assembly.
  Speaking to BBC Radio Wales' Sunday Supplement programme, he added: "This thought came to me when I was having an innocent conversation with a fellow farmer, we were talking about Brexit.
  "He posed the question to me that if the referendum for the assembly was re-run today, could it be won?
  "If you reflect on it and the state of politics at the moment, I don't think it could be won, to be honest with you.
  "The more and more you travel around Wales, and I say this with a heavy heart... sadly people feel very remote from the institution.
  "While people indicate in polls they want decisions taken here in Wales, it's not necessarily through the vehicle of the National Assembly."
  Two referendums were held on Welsh devolution. The first, in 1997, established the Assembly with a victory for Yes - 50.3%.% to 49.7% - but on a turnout of 50.1%.
  The second in 2011, on whether the assembly should have powers to make law in areas it has jurisdiction, was also won with 63.5% of the vote but with a turnout of 35.6%.
  Plaid's Ms Wood said: "Brexit provides an opportunity for the nations to take more power and responsibility from the UK.
  "The referendum result shows how Westminster rule has left many communities behind. It should in no way be interpreted as a vote to centralise more power in London.
  "No self-respecting country should be timid or ashamed of governing itself. It's disheartening to see such a negative attitude from some in Welsh politics."
  A spokesman for the first minister said: "We have announced our key priorities for a future (Brexit) deal, established a new business confidence fund to help businesses through this uncertain period and we've announced the establishment of a new department in government, alongside a new external EU advisory group.
  "We've met with the prime minister, chancellor, Brexit ministers and the agriculture minister - we've brought together all the devolved governments in Cardiff and summoned a special Council for Economic Renewal. We have demanded, and secured some certainty about future funding, though there is still a way to go on that.
  "The narrative the Welsh Tories want to develop simply isn't borne out by the facts."
target: Welsh voters would turn down devolution now if a referendum were held on the assembly's existence, Welsh Tory leader Andrew RT Davies has said.