Short answer: there is no evidence it does.
During the Voice referendum campaign a common view has emerged that a success for the No campaign will be bad news for the federal Opposition and its leader Peter Dutton for the next federal election. The theory is that the Coalition's opposition to the Voice is already tying it to some strident political positions and that it will wear the blame for the defeat. An example of this was a recent George Megalogenis article that initially claimed there was no precedent for an opposition leader taking down a referendum and winning the next election or the one after (which was edited after I and perhaps others pointed out Menzies winning in 1949 after defeating the Rents and Prices referendum in 1948). Similar themes have also been present in the commentary of Professor Matt Qvortrup (who has incidentally long predicted that the Voice would lose, albeit recently with what looks like an optimistic Yes vote of 48 +/- 2.5%). Prof Qvortrup, who has great experience with overseas referendums, may well have evidence that referendum-defeat boost is a big trend overseas, though at a quick look I did not find any study to this effect.
So, is there anything in this for Australia? The paradigm case is supposed to be the 1951 defeat of the Communist Party ban referendum, in which Labor won the battle but lost the war: things said on the referendum trail made it easy for Prime Minister Menzies to tie them to Communism for many years after. This narrative, however, seems simplistic to me, because the Opposition Leader (Evatt) not only said and did things on the referendum trail that made it easy to tie Labor to communism for campaigning purposes, but kept saying and doing such things forever after.
