I have been researching the same question, and would like to know if invitations do expire.
I found a reference to a System Property that might have some relationship to the longevity of an open invitation ... could Jive Support person please weigh in?
Undocumented Jive System Properties for discussion of user.decay.period
Specify the number of months that should pass with no login activity before a user account is automatically disabled. (Set this value to an arbitrarily high number such as 1000 to effectively disable the UserDecayTask). Requires restart.