Rerelease the Song

Sometimes, an artist will want to give a song a second chance. Maybe it just didn't pan out as a single the first time, or maybe it's just so good that it needs another release.

Distinct from Rearrange the Song in that the re-release isn't always a re-recording, although the two tropes may overlap.

Examples of Rerelease the Song include:

Randy Travis' first single for Warner Bros., "On the Other Hand", flopped upon initial release. After its followup, "1982", became a top 10 hit, he persuaded the label to re-release "On the Other Hand". The re-release became his first #1 hit.
Similarly to the above, Chris Young released "Voices" in 2008. It barely made the top 40, but the next two singles after it went to #1. Based on the momentum of those two, he asked to re-release "Voices" in 2010... and in February 2011, it became his third #1.
Keith Urban found that "You Look Good in My Shirt" (from the album Golden Road) was getting positive reception whenever he played in concert, and several stations were playing it even though it wasn't a single at the time (the unsolicited airplay even got it on the charts). He re-recorded the song in 2008 and released it from a Greatest Hits Album.
And around the same time, Brad Paisley re-recorded an album track, "Waitin' on a Woman", and released the new version as a single.
Alan Jackson wanted to release "Home" from his debut album, but decided against it because another singer had a song called "Home" out at the same time. He later included the original on a Greatest Hits Album and released it as a single in 1996.
- And later on, he re-recorded "A Woman's Love", an album cut from 1998's High Mileage, and released the re-recording in 2007.
Pam Tillis first released "One of Those Things" in the 1980s when she was on Warner Bros. It didn't chart. She later re-recorded the song for her first Arista Records album, and the re-recording was a top 10 hit.
Obscure 80s band Sheriff made "When I'm With You" in 1983; it flopped and the band broke up. A DJ started playing the song again in 1988 and it shot to #1.
Peter Andre's 'Mysterious Girl' may feel that it's been re-released multiple times (what with having 14 different versions released over various mediums) but it's only been re-released once in 2004.
Switchfoot's "I Dare You to Move" was the first track from their album Learning to Breathe. Feeling that "that song hadn't lived its shelf life yet", Switchfoot re-recorded it (but the new version sounds so much like the original version, you really have to pay attention to hear the difference) for their next album The Beautiful Letdown. This turned out to be their breakout album, and "Dare You to Move" became a certified-gold single.
Jimmy Buffett did this with his song "The Captain and the Kid" (about Buffett's childhood relationship with his grandfather, a retired cargo ship captain), which first appeared on his less-than-successful second album "Down to Earth". It was later included on Buffett's much more successful seventh album "Havana Daydreaming", where it was released as a country single. It was released for a third time on his even more successful greatest hits collection, "Meet Me in Margaritaville: The Ultimate Collection".
Steve Wariner's first single was "I'm Already Taken" back in 1978. He re-recorded and re-released it in 1999.
Kenny Chesney re-recorded his 1994 single "The Tin Man" for his first Greatest Hits Album and released the new version in 2001. The re-release has the distinction of being his only single release of the 2000s not to reach Top 10.
Anberlin's "The Feel Good Drag" was a track off their 2005 album Never Take Friendship Personal that the band liked and regretted never releasing as a single. They re-recorded it a few years later to be the first single off their major label debut, and it became their biggest hit.
For some reason, Garth Brooks decided to release "Wild Horses", an album cut from his 1990 No Fences disc, in 2001.
From 1986 to 1992 there was a major trend of rereleased songs becoming big hits in the US, including three that hit #1 (the aforementioned "When I'm With You", "At This Moment" by Billy Vera & The Beaters, and "Red Red Wine" by UB40). They generally fell into two groups: Revival by Commercialization ("At This Moment", "Stand By Me"-Ben E. King, "Twist & Shout"-Beatles, "Do You Love Me?"-Contours, "What a Wonderful World"-Louis Armstrong, "Unchained Melody"-Righteous Brothers, "Bohemian Rhapsody"-Queen), and Top 40 stations putting older songs into their rotation ("Red Red Wine", "When I'm With You", "Where Are You Now?"-Synch, "Into The Night"-Benny Mardones).
Jake Owen originally recorded "Eight Second Ride" for his debut album "Startin' With Me." He re-recorded it for his second album "Easy Does It" and released it as a single.
Fleetwood Mac's "Landslide" first appeared on their 1975 self-titled album. A live version, which appeared on their 1997 album The Dance, was released as a single in 1998 and peaked at # 51 on the Billboard Hot 100.
Dolly Parton released "I Will Always Love You" twice: in 1974 and again in 1982. Both versions went to #1 on the country charts. She recorded a third version in 1995 as a duet with Vince Gill, which got to #15 despite not being released as a single.
Dog Days Are Over by Florence + the Machine got re released in early 2010 with a new more to theme video.
Kelly Clarkson re-recorded her 2005 single "Because of You" as a duet with Reba McEntire. The duet version was sent to country radio in 2007.