I vaguely remember that it had something to do with bards and storytellers. I thought the foundation was similar to Norse mythology. People telling stories to explain things, teach lessons, and pass the time.
That was a theory for why Zeus was such a womanizer. As the mainstream strong version spread, it swallowed up the small local religions. The best way to settle the disconnect was to have Zeus hook up with the god or hook up with someone and have them give birth to the god (or a swan, or grass, or anything...they basically just hooked up and drank wine...pretty close to standard elite debauchery).
I also think that their ceremony must have helped too. They didn't really do a whole lot that was too bad. Most of the ceremonies were fairly festive. The sacrifices were just big barbecues. They ate all the good meat and "sacrificed the fat to the fire."
*I think...I remember it in the Odyssey, but that may have been heavily influenced by Roman tradition...hard to split them up at times.
With all this in mind, it's pretty easy to see how they held onto it. It was a popular and vague religion without much to offer as a substitute.
I don't think that they had a stranglehold on it though. There were a number of cults and foreign religions that took hold on a smaller scale. A few philosophers also formed what amounted to atheists groups that got together and partied because life was too short (The Followers of Dionysus did the same thing though).