"Why should one side of the argument (i.e. retaining the status quo) have a considerable advantage over the other (voting for change)? If such a condition should exist why should it be for retaining the status quo and not for enabling change?"
As to the details of the question -- well, let's try to set the obvious recent referendum on the EU aside, as it's obvious that any discussion on how referenda should work might be influenced by your perspective on that. Obviously I'm annoyed that a rule that could, and perhaps should, have been in place wasn't and allowed something to happen that I didn't want -- but, to be clear, I accepted the result at the time, and when I voted it was in an understanding of the rules and the potential consequences, and I am not attempting to undermine the legitimacy of that referendum.
Still, the fact is that most countries that have referendums as a constitutional norm tend to have rules alongside to effectively demand that serious changes can't be imposed just based on 50%+1. The "status quo" is protected because -- well, because it seems to be common sense that if you are going to implement serious changes then you had better be as sure as possible that the country is on-side with those changes. That means that you could require a reasonably high turnout (not really an issue in 2016, as it was about 72% I think); or some sort of enhanced majority; or a supermajority in another sense.
In Switzerland, where referenda are just a part of the system, the minimum turnout requirement for a positive result to be implemented is 40% (so not outrageously high). The majority requirement is still only 50%+1 but (perhaps in order to protect less populous regions from the "tyranny of the majority", in a similar spirit to the electoral college of the US) there also has to be a majority of the cantons in favour of the proposal for it to pass. If the rule had applied in the UK then -- well, it would depend on what our equivalent of "Cantons" was as to how it would have impacted things.
But essentially the aim of requiring more stringent conditions for referenda isn't to stifle the electorate from getting what they want but to try and ensure that significant national changes have broad popular support across the entire country. Perhaps because the UK doesn't really do referendums, except when it's politically convenient (the three most recent have been, essentially, to try and get the Lib Dems into a coalition, to satiate the SNP and get them to shut up, and to bring UKIP-leaning voters back to the fold in 2015 and take on the Eurosceptic Tories), then we never really got around to writing rules that are, in fact, the standard across those democracies that hold referendums.
There are a few other arguments either against referenda altogether, or at least in favour of tightening the conditions for victory for the "change things" side, although some of them stray a little too far into the "Hitler did it so we shouldn't" argument.