Whilst a new referendum might not be "the way forward", at least it is not the way backwards into the Nineties (or earlier).
We don't have to "beg to be taken back" now, we are still full members of the EU, nothing new is implemented, no one can force UK into Euro market... for now, until the article 50 is triggered. Later all will depend on trade negotiations, which look rather gloom after UK failed to achieve much in previous negotiations with the EU.
For those of you who doesn't want to challenge the outcome as “it’s democracy in action” - it is, but DEMOCRACY ENDS WHEN PEOPLE DON'T HAVE LEGITIMATE WAYS TO CHALLENGE DECISIONS, NOT WHEN PEOPLE WORK ON WAYS TO CHANGE THEM. You are able to vote differently in next general elections after discovering that a politician was blatantly lying, but not so in this case. In such a serious, world reshaping and irreversible matter, isn't it reasonable to double check voters’ wishes? Or do you think that democracy will stop working in the second referendum?
"People have spoken" - yes, and they have been indeed heard this time, which is good. The question many now ask is if it indeed was the EU they were voting against, or domestic UK politicians who never listened to them?
“It will mean endless referendums” or even “you accept democracy only if it suits you” - the second referendum is needed not because the result is "right" or "wrong", or doesn't suit someone, but because it was so ill thought about. No next steps were ever considered even by leave campaign leaders, not mentioning voters. By the time the new referendum takes place, some of the consequences (both negative and positive) will be seen, a plan of separation from the EU should be created, so people much less likely will be voting just for a fairy tale. It is generally accepted that many people are able to learn after just one serious mistake, so both voters and politicians would act more responsible.
Civil unrest because of far-right groups being angry - As we could have learned from History, a certain, and bigger, unrest will happen if no one dares to tell that extreme nationalism is not a card to play any more.
"We will look weak if we back up now" - well, it's a difficult choice between looking weak and looking stupid. More seriously, it would be difficult to work with the EU again, but most probably less difficult then trying to negotiate good trade deals with angry EU leaders now.
"If struggle means just no TV, it's a joke" - nowadays the wast majority of people, unfortunately, will sacrifice many more important things before a TV: environment, culture, education and, funnily enough, medicine. So the situation with no TV also means lack of all of the above.