That depends on how well they were able to set themselves up, and what kind of technology they had to begin with - I'm seeing a lot of assumptions that there were any stations or cities at all, when it could have just as likely been basic settlements still establishing themselves with old technology. The ships wouldn't have to be broken, they just have to run out of the resources needed to run them, and without those resources from earth, new ones would have to be harvested in new eden to accomplish the task. That would take time. Over time, ships would stop travelling and the colonies would gradually forget one another existed.

Fortunately, your cynicism is not a case against a good story, but it is a pretty good defence against poor comprehension, because it explains your ignorance based on your sheer desire for something to complain about - but you missed the part where I didn't say there were no resources in New Eden, but rather, the settlers would have been ill equipped to harvest them for some time.

What a lot of people don't remember about the collapse of the EVE Gate when they're done reading is that it didn't just close.

It collapsed violently, and almost obliterated the entire system of New Eden with an enormous release of energy that decimated most of what was originally there, including most of the settlers. It's reasonable to assume that the sheer amount of energy released could have destroyed or fried a lot of the electronics for several systems over once they were hit with the blast wave.