Welcome to political gamesmanship. That very thing happens all the time.
What are the rules about getting a referendum on a ballot? Whatever the rules are that got the exit on the ballot, why does this break these rules and prevent another referendum from ever getting on a ballot again? And why can’t that be a referendum to reverse a previous referendum?
Here in California, referendums make it to a ballot every two years that gather a certain number of signatures. Say one gets passed that legalizes heroin. Are you saying that another referendum should not be allowed to make it to the next ballot 2 years later that reverses this even if it gathers enough signatures?
I think the UK system is a bit different to the US. The UK (and Australia) very rarely hold referenda, and it is not simply a matter of getting a number of signatures. I really can't be bothered looking at it more thoroughly, but a referendum is almost a matter of consent by the people through prolonged pressure - the UK has only had 2 -3 of them in total.
Lets use a different example than yours.
In Australia in 1967 we held a referendum to give Aboriginal people voting rights. By the time it was done it was already a foregone conclusion due to consistent long running pressure, and got a yes vote.
Now, if the Australian government had then started adding on other things like making Aboriginal people kings with absolute power over whitey, then started handing them billions of dollars and millions of acres of land, then said, let's revote and people voted no, is that legitimate?
It's not the role of government to punish wrongvote and force people to get it right by tearing everything down. It seems like a really dangerous precedent to set to me.
The government should hand negotiations to people who are qualified and pro Brexit.