Persevere received some mixed reviews. AllMusic's Jon Azpiri remarked that although the album was "not likely to achieve the kind of success of their previous work", that it had "enough interesting material [. . . ] to prevent [the band] from being placed in the "Where Are They Now?" file", and praised "There's a Touch" and "Land fit for Zeros" for having "the same goofy charm" as the group's biggest hit, "I'm Gonna Be (500 Miles)". In 2001, Bill Holdship of Rolling Stone stated that "the new album is quite good, combining folk, soul, country and pop with the Fifties-styled melodic sensibilities of the brothers Reid", observing that the song "One Too Many" would "make The Eagles green with envy". In Riverfront Times, Steve Pick was praising of the record, commenting that the band "have equaled the musical triumphs of Sunshine on Leith" and deliver "a series of snapshots that reveal the actual experience of life during middle age, when love is more complicated than it seems".