Wiktionary
vb. 1 (context intransitive English) To persist in. 2 (context transitive English) To constrain (a person) to continue doing (a task).
Usage examples of "keep at".
He would have understood then that in her eyes he never had been, was never like to be, aught but a servant--and one, hereafter, that, deeming presumptuous, she would keep at greater distance.
One thing he didn't want to be doing was chasing after the man who ruled the Universe, who was only doing a job which he might as well keep at, because if it wasn't him it would only be someone else.
Those who genuinely desired the lonely life could have it, of course, but there was no guarantee that they would make enough to keep at it for long.
A more poetic way of saying forever, perhaps, or expressing an indefinite, like: We'll keep at this project until midnight at the Well of Souls—.
You had to love space to keep at that sort of job over the years, but there was something in the human psyche that craved clean air and openness, and when they got the chance they wouldn't take a covered or cloistered ride for anything if they could help it.
You keep at it, being holy and perfect, and you one day become a little god yourself, or so the system says.
The daughters they keep at home until they become marriageable, and then they bestow them upon some of the men of the other island.