In fairness, it's very difficult to ignore the charge that a second referendum could be undemocratic, because that debate helps to shape the question. For example, OG's version, ie a vote between two versions of Brexit, is equally arguably an undemocratic choice*, by removing one option from consideration. Then again, having a straight three-way fight between two versions of Brexit and remaining probably risks splitting the Leave vote and allowing Remain to win, unless some rule is put in place that requires the decisive option to obtain 50%+1 of the vote.
If Parliament cannot find a majority for any given version of Brexit, or (if such a version does after all exist) if Government is incapable of negotiating it in time, that at some point the only sensible resolution is to return the decision to the people. Otherwise, we end up with the most undemocratic option of all: namely, a future that not even Leave voters wanted, let alone Remainers.
*Citation: I have argued this