Well, for a start they've hardly "swept across Libya" in a "short time". Tripoli fell amazingly quickly, but that was largely because Gadafi deserted with a large number of his forces to Sirte and further south. Recall also that many of the towns in the main part of the war also took ages to be liberated, several changing hands more than once.
Two possible reasons I think why Sirte has resisted so long:
(1) Those Gaddafi-ites holed up there are probably, a lot of them, war criminals, and are desperate to avoid capture/defect.
(2) The rebels (if we still call them that) are reluctant to launch a total assault for fear of injuring civilians: they've given several deadlines to allow the fighters time to surrender, and civilians to leave.
Also this is no conventional fighting force. They seem to be operating a "nine-to-five" style of attack, arriving for war in the morning and leaving to get home for tea in the evening (!)