Yes, they certainly can last a long time. I know people who have had to carry on their online relationships for years until they found a way to be together. My own online relationship only lasted six months...before he was able to move here, marry me, and make a family with me. I think that in a lot of ways you can learn to get to know people a lot better online than if you'd met them offline -- you have to talk in order to have time together, so the physical aspect doesn't get in the way of getting to know each other. That's not to say that they will all last, relationships in general -- both online and offline -- have a pretty low batting average, but they certainly can.
@ dexixy -- most people online are psychos...aren't you online too? Everyone has a past of some sort, and someone can hide their dark past just as easily in person as they can over the internet if they have a mind to do so.