The living on this show, all have the zombie virus correct? So we get to the end, civilization starts to come back, survivors die, and now more zombies. Their children I would assume would have it passed on. Unless they find a cure for the plague in the show, is everyone pretty much screwed forever?
Remember that, according to Mr Kirkman, the show takes place in a world where zombies didn't exist in pop culture prior to the apocalypse, which is probably a big part of the reason why the zombies were able to take over so effectively in the first place. Nobody knew what these things were or how to stop them. Tara famously kept shooting her upstairs neighbours in the chest time and again, because as a cop she had been trained to aim for the center of mass. I think it's probably true that nobody will ever find a cure to the zombie plague, but that doesn't mean humanity can't rebuild civilzation on a global scale. It just means we have to adapt to the fact that dead bodies will get up and try to eat us from now on ;)
For example, funeral arrangements will need to be made more quickly, as some people can turn in a matter of hours. Open-casket funerals will likely stop happening, and cremation will likely become much more popular. Combat techniques will focus more on headshots where possible. Law enforcement - and probably a lot of other people - will start carrying machetes to cut off the heads of any random bodies they find (or create!) Once we get back up to a level where laboratory research can kick into high gear, there will probably be a lot of time and money spent on finding ways to detect people who are in the process of turning (due to a zombie bite/scratch or that weird zombie flu from season 3 (4?)) - as well as a cure, yes.
Of course, people will occasionally die unannounced and turn before anyone finds the body. Terrorists will probably start releasing a small number of zombies in a populated area to cause panic. There will be smaller outbreaks from time to time. Zombies will always be a threat, but I think civilization could adapt to deal with them and keep their numbers low. If we can keep a lid on nuclear weapons, wild animals and other humans, we can probably manage zombies, once we know what to expect. You can already see this happening in the show, where the zombies are mostly an afterthought in recent seasons. They're a chore to deal with, but other humans have been the real threat to the protagonists for a long time now.
They will come to adapt to making sure the brain dies when people die and they wont come back so there may always be a small problem with them but it will become more manageable as more zombies get killed off and more people take care of their dead properly. They have shown this in previous episodes when someone dies and they go and make sure that the brain is dead. And as a race we are problem solvers. Civilization will continue to ponder this question and come up with better ways and better ways we are survivors "we will re infect this Earth that's what we do!".... And who knows maybe beer IS the answer! (Jim the Brewery guy that Morgan finds with a bag over his head being chased by walkers in a field, in fear the walking dead)