Obviously asking the electorate their opinion on the terms of the UK leaving via a second referendum would not be asking the same questions on the ballot slip. It would therefore not be a re-run and is a perfectly democratic process given what is now known about the implications of leaving.
The referendum did not spell out the nature of the future relationship with the EU nor the consequences of Brexit. Voters are likely to have a clearer idea of what is on offer at the end of the negotiating process.