Join Date: May 2004
Location: Wilmington, DE
Bikes: 1984 Trek 660, 2003 Specialized Hardrock, 2004 LOOK KG386i, 2005 Iron Horse Warrior Expert, 2009 Pedal Force CX1, 2014 Islabikes CNOC 14 (son's)
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Most likely cause is an excess of friction on the derailler cable, whether from corroding/damaged housing, an out-of-place ferrule, or something wrong with the under-the-bottom-bracket cable guide. Most likely the first though, especially if the bike has been used for several thousand miles, in the rain, or near the ocean. Other additional causes could be a binding derailler or a bent derailler hanger. You didn't mention severe use and you didn't mention dropping the bike so I'm not thinking either of those is the problem.
When you change out the housing and cable you'll be resetting the tension on the rear derailler. Read up at www.parktool.com
and follow their instructions to the word and it should go smoothly. Attempt to take shortcuts and expect to be at it for a few days. If the bike shifted good at some point and you have not yet touched the limit screws, do not touch them. They never go out of adjustment.