There is no guarantee a second referendum would heal divisions. If the public votes to remain in the EU, which polls indicate it will do, then that would mean there has been one vote to remain and one to leave. This would only fuel uncertainty and division. Instead of silencing remainers, it would empower them.
In that case, where would it end? Would we have a best of three referenda? Or would Brexit turn into a tennis match with a best of five series?