I don’t think there should be a “second referendum” in the sense of simply repeating the question asked in the first one. The British people already expressed a response to that question, and it would make a farce of democracy if you could simply re-run a vote just because you didn’t like the original outcome.
However, the deadlock in parliament is no longer simply a question of “Leave or Remain”. Now that a particular withdrawal agreement has been negotiated, it is a question of “Deal or No Deal (or neither)”.
For that question, I think we do need a referendum. Without it, parliament will either impose Theresa May’s Deal upon us, or lead us into a no-Deal Brexit, or extend/revoke Article 50 without the public having given their explicit consent to any of these outcomes.
Without a referendum, MP’s own career aspirations, party politics, faction rivalry and parliamentary arithmetic will continue to be prioritised over the actual public interest, and this will be reflected in the final decision on Brexit.
As a side note:
Whilst it is true that most Remainers want a referendum (as that is the only chance for them to legitimately get their way), it is not true that a referendum would automatically lead to a “Remain” outcome, as people so often apparently assume. It would simply lead to whichever result is favoured by the majority of the British people at the time.
Furthermore, in order to be impartial regarding the decision as to whether or not we have a referendum, we should not assume a particular result from beforehand. We must simply determine whether or not a referendum is in the public interest. In this case, I believe it is.