I see some proposals that have been languishing here for over 7 years at this point, so I'm curious as to what is the longest amount of time a successful launch has spent here, from initial proposal to successful launch.
Two years is the longest a proposal can exist unfinished.
Proposals have one year to complete the Definition phase, then another year to complete the Commitment phase; otherwise, they are closed as inviable and eventually removed. After a short, private beta (typically less than 30 days), proposals become fully launched, public sites.
Your confusion lies in our misuse of the word "beta" to classify smaller sites. These are fully launched sites, but unless they reach a substantial size (sustaining about 10 questions/day), the current system says they they retain their beta label forever. It gets even more confusing when a smaller, perfectly healthy and stable site is is said to never "graduate", which is when a site is given a custom design (mixed in with a few other necessary features, which is why we came up with "designless graduation"). Oy.
I've been a big proponent of ending this collection of confusing labels and the community frustration that comes with it, but after collaborating with the Community Team on a better system, the project was summarily vetoed and scrapped in the last hour.
I'm getting a bit off topic here, but for further reading, I wrote about how this improved life cycle would work many times. See: