The only way a 2nd referendum would be undemocratic is if it gave the public no room for change or debate afterwards, but frankly even if we voted 60 - 40 in favour of remain in a Remain vs Leave (without a confirmed deal on the line, just ensuring what the public wants) I doubt that'd be the end of it.
There's literally nothing undemocratic about asking the public whether they still want to leave the EU. It's the same people voting with the same stakes on the line, just this time we'd know more about the options than we did the first time.
The deal with people calling a 2nd refendum) and the EU elections that decide who represents the UK in the EU undemocratic is that they are, to put it bluntly, full of sh**.
It's not at all undemocratic to have a public vote, they just screech as hard as they can that it is undemocratic so that their followers believe them and blindly march into the black-hole of nationalism.