Green’s Dictionary of Slang

cock n.6

[? link to phr. that cock won’t fight, used of someone/something undependable]

a horse, backed as a favourite by the public, which either fails to run or, if running, fails to race hard.

[UK]Sporting Gaz. (London) 8 Apr. 4/3: Cock — A horse who is not trying to win [...] a ‘stiff ’un’ .
[UK]Sl. Dict.