Sounds like a similar issue as happens with a motorcycle with a throttle cable getting stuck. Is it a dual cable (push/pull) arrangement or just a single cable? Description makes it sound like a single cable. I'd remove the cable and check for kinks or crimps along the sheath.
If none then there could be some deposit inside the sheath that is making the cable bind. To clean that out I would first get some WD40 into the sheath and then work that cable both ways through the sheath as much as you can until you feel it moving freely. Then follow that with some grease, getting it down inside the sheath as much as possible and work the cable both ways through the sheath to work the grease all the way along the cable.
If there are any kinks or crimps along the sheath, or if an inspection of as much of the cable as you can see shows any bend or fraying of the braided/twist of the cable then replace it.
Hope this helps a little.
Oh, and welcome to the forum datamatt.