Depends on what you mean by an extended period of time. Once the original League was shuttered by Aquaman during the JLDetroit era, no one has had an uninterrupted run as a member, including Hal.
Hal was a member of the League from 1960 to the early 80s, at which point he was exiled to space, returned, then quit and clawed his way back again. During that period, John filled in a bit, before Guy took over for the Bwa-Ha-Ha JLI era.
When that ended, Hal resumed his membership and assumed leadership of the JLI until Emerald Twilight happened, then Kyle took over for a few years, then John again until Hal resumed his membership for another several years until early on in the New 52, only to return again at the end of that era for Darkseid War, after which Jessica & Simon took over for a bit until Hal returned for Metal, then passed the reins to John again. And, if we count all the big events that have taken place since Legends, Hal has been the main GL in every single big event, barring the times when he's been dead (and, even then, he often showed as the Spectre).
I can't say Hal has been underserved as a member of the League. Only Superman, Batman, Wonder Woman & Flash have more issues as a member than him.