They absolutely have one, but unlike Auburn's it isn't targeted at any particular program. Like Auburn's (and LSU's too, when they underachieve) struggles occur in large part because of Alabama. Alabama simply has been able to recruit more of the players that all 3 of those schools covet.
Georgia, meanwhile, hasn't underachieved because of any specific program. Georgia's biggest conference rival, Florida, has not been a juggernaut since the late 2000s, so it isn't because of them. Their other conference rival, Tennessee, has been near-complete garbage for over a decade. Another rival, Auburn, has been the up-and-down, inconsistent program they always have been. The dynastic program of the last 10 years, Alabama, has been located in the other division; Georgia does not play Alabama every year or even recruit directly against them all that often. There really is no valid excuse that can be offered - at least Auburn and LSU can say "Well, we're trying to compete directly against the greatest coach the sport has ever seen, in the midst of the great run of dominance the sport has ever seen."
They've failed to reach the top sometimes because Florida beat them, Alabama beat them, LSU beat them, or even because they stubbed their toe in an unexpected loss against South Carolina or Tennessee.