The idea that we vote on things and then just keep voting on them multiple times until the wanted result is achieved doesn't sit well with me. The impact of Brexit to my area of interest (UK research) is very likely to be profoundly negative and I don't want to leave the EU primarily because of this. That said, if we don't honor the outcome of a referendum then the impact will be profoundly negative on democratic process overall and that would be even worse in my eyes.
I mean that's how real elections would do it. You keep voting 'til you get an actual majority (or you come to some sort of coalition agreement).
Referendums are so much different than regular voting.
While voting for a MP/PM/President is important, it's a vote for a representative to make decisions for you, and it's one of many representatives. In other words, there's plenty of safety nets in place no matter who the PM/President is.
Referendums aren't like that at all. People literally vote on a decision that should be relegated to the experts voted in by the public. The UK population probably didn't understand that.