A poor launch can set the stage for YEARS
It is not uncommon for me to get a call from a prospective client and hear something like: "We launched a new AMS last year, but it was a rushed implementation. We never really got things right from the start and now everyone is unhappy."
Too often, when an implementation is rushed (e.g., not enough time provided for data conversion, or training, or testing), the result is that the launched product doesn't work as expected. This could be true on either or both the staff side or the customer-facing side.
Obviously, this isn't good, but the significant downside to a poorly executed launch can be the long-term lingering distaste (or outright hatred) of the new system. Because the launch was rushed and staff was unprepared for go-live, staff winds up hating the system. This means that user adoption will be lower, which will affect the long-term success of the system. I've even seen situations where staff actively avoided the system (setting up their own shadow systems) because they so distrusted the new AMS.
The sweet spot is to give yourself enough time to complete a solid implementation without causing the project to go on for too long. And if you can avoid it, never launch an AMS before a major event, like an annual conference or annual dues renewal billing. As I like to tell my clients, we're looking for the "least bad time" to launch.
Your AMS launch is your first big leap into a new system and new experiences for (and attitudes from) staff and customers. So make sure you get it right.