From Longman Dictionary of Contemporary Englishkeep at something phrasal verb1 keep at it spokenCONTINUE/NOT STOP to continue to do something, although it is difficult or hard work I know it’s hard, but keep at it! Don’t give up!2 keep somebody at somethingWORK HARD to force someone to continue to work hard and not let them stop → keep→ See Verb table
Examples from the Corpus
keep at • The animals were kept at 20°C, 50% humidity and a light/dark cycle of 12/12 hours.• The population were kept at a pre-technological level of civilization, with android advisers to make their lives easy.• Velvet can be kept at bay by good husbandry.• As a criticism of the modern world, Fantasia of the Unconscious is a book to keep at hand and re-read.• In those optimistic times, the commission thought that if they just kept at it they could eventually eradicate the gypsy moth.• Getting a novel published has inspired White to keep at it.• Hence Phoenix always keeps at least two of its garbage districts in public hands-so it will always have the capacity to compete.• We kept at them and finally wore them down. 