Green’s Dictionary of Slang

never stand still n.

also can’t-keep-still
[rhy. sl., accentuated by the endless movement of the machine]

a prison treadmill.

[UK]‘Doss Chiderdoss’ ‘The Rhyme of the Rusher’ in Sporting Times 29 Oct. n.p.: The once a week made me go ta-ta / For a month on the can’t keep still.
[UK]J. Franklyn Dict. of Rhy. Sl. 46/2: can’t keep still Treadmill. 19 C.
[UK]Partridge DSUE (8th edn) 179/2: ca. 1850–90.