Is a single expiation for an oath sufficient for me, or is an expiation required for each time I miss congregational prayer, based on my vow to pray a number of rak'ahs equal to the missed prayers, with my intention of repetition by saying "whenever I miss a prayer"?

Your vow is a vow of obstinacy (nadhir lajaj), and its maker has the choice between fulfilling what he committed to, or offering an expiation for an oath (kaffarat yamin). If you choose the expiation, a single expiation will not suffice for the entire vow, but rather for the prayer you missed in congregation. And every time you miss it again, another expiation becomes binding upon you, or the fulfillment of the vow.