It seems that these "marriages of convenience" have a way of working themselves out. On average the football only agreements have lasted less than four seasons. Only twice has a football only affiliation lasted more than 7 seasons.
Walking through them in order, all dates are the date play began and ended unless otherwise noted:
Big East: In 1991 the Big East added West Virginia, Rutgers, Virginia Tech, and Temple football only. Four years later WVU and Rutgers became all-sports members, 10 years later Va.Tech became a full member and 11 years later the league announced Temple would be expelled after their 14th season in the league.
Big West: 1999 Arkansas State returned for two seasons in the Big West ahead of the formation of the Sun Belt.
Sun Belt: 2001 the league formed with Idaho and ULM as football only members. Idaho accepted a full membership effective 2005 but withdrew to join the WAC. ULM joined as a full member in 2005.
Sun Belt 2003: Utah State joined football only and like Idaho accepted a full membership before withdrawing to join the WAC in 2005.
Mid-American Conference: 2002 Central Florida came in for football only and departed after three seasons for C-USA.
MAC: 2007 Temple joined the league football only and left after five seasons for the Big East.
Big East: 2012 Navy announced as a football only member, will enter in 2015. East Carolina was announced as a future football only member, four months later they were extended full membership.
MAC: 2012 UMass joined football only and has recently been expelled effective after the 2015 season meaning their time in the league will have been four years.
Mountain West: 2012 Hawaii joined football only and is currently still a football only member.
Sun Belt: 2013 announced Idaho and New Mexico State as football only members starting in 2014.