You
can flip any argument, but there isn't real symmetry here.
If a change would be large and far-reaching and painful to undo, then it should be more difficult to make. Not impossible, of course: sometimes you need to make large far-reaching hard-to-undo changes. But imagine the following situation: about half the population likes X and about half hates it, and every year we hold a referendum on whether to have X or not. Then about once every two years you flip between X and not-X and all the upheaval costs you more than the gain from whichever is the better choice would get you.
So before making a big upheaval-inducing change on the grounds that The People want it, you should have good evidence that The People really do, which means one referendum with a result much more decisive than 51:49, or maybe a series of 51:49 referenda all going the same way.
If I were setting up something like this and could choose the rules, they would be something like: we run a referendum every couple of years until we get a decisive result; a side that won the last N referenda needs a 20%/(N+1) margin to get its way. So, first time round you need to be 60-40 ahead to settle the question; if you won the first time then you only need 55-45 the second time; if you win again but still more narrowly than that then you only need about 53-47 next time; etc. If one position really does consistently have majority support it'll win eventually even if its advantage is narrow. If public opinion is very changeable then too bad, a decision will have to wait until The People have a strong enough opinion to measure with confidence.
(Obviously nothing like that will ever happen. Too geeky and complicated.)
Of course, that wasn't the only major problem with the Brexit referendum. The other catastrophic problem was that it was a choice between "stay in the EU", a well defined outcome with known good and bad points, and "leave the EU somehow", something that could mean dozens of different things. It should have been between "stay in" and "attempt to negotiate terms for leaving, and then hold another referendum on whether to go ahead". Or between "stay in" and "leave on such-and-such terms if we can get them, and otherwise ask again". Or the government should have held extensive negotiations first on what terms it could leave on, and then held a referendum on whether to leave on those terms. Or the referendum could have offered options "stay regardless of terms", "leave regardless of terms", and "leave if such-and-such terms can be achieved". Those possibilities are all pretty unsatisfactory, but they're all better than choosing between the status quo and An Undertaking Of Great Advantage But Nobody To Know What It Is.