"draw out or lengthen in time," 1530s, a back-formation from protraction and in part from Latin protractus, past participle of protrahere "to draw forth, prolong." Etymologically identical with portray, which is the same Latin verb altered in passing through French. Related: Protracted; protracting. The English verb survived chiefly in the past-participle adjective.
Protracted meeting, a revival meeting continued or protracted ; a series of meetings of unusual importance, often lasting for several days and attended by large numbers ; chiefly used by Congregationalists, Methodists, and Baptists. [Century Dictionary]
The phrase is attested by 1832.