1
general::
Scruple or hesitate, as in She sticks at nothing to gain her ends. This idiom, nearly always used in a negative context, was first recorded in 1525. Also see STOP AT NOTHING.
American Heritage Idioms
2
general::
Phrase(s): stick at something
to keep trying to do something; to stay on a task or job. • I hope he can stick at this job. • He doesn’t seem to be able to stick at anything for very long.
McGrawhill's American Idioms And Phrasal Verbs