The AllMusic review by Thom Jurek awarded the album four stars and said that Love Is What Stays "is a deeply satisfying and, in places, even astonishing reflection on time and its passage. Memory, reverie, regrets, victories, hipster mysticism, and wonderfully canny theatrically poetic wordplay all come to bear in these songs. It is more adventurous and downright wily in its aims than anyone could have hoped for."[1] Jurek says that music fans looking "for true authenticity and artfully made American popular music, should snap this up as quickly as possible. Time will be the judge, but Love Is What Stays may become a Murphy masterpiece and - let's face it - the man embodies the very essence of "hip." And always will."[1]
The Penguin Guide to Jazz Recordings review assigns a rating of ***(*), meaning "an excellent record, with some exceptional music" which is "only kept out of the front rank by some minor reservations".[3] Richard Cook calls Murphy's performances "clever, worldly wise, emotionally unguarded singing of a very high order", but says, "The only reason to dislike it is that the band sounds cold and not as smart as the boss".[3]
