The term 'BOTHERS PERSISTENTLY' can be broken down into four crossword solutions: NAGS (4 letters), PESTERS (7 letters), EATSAT (6 letters), and NAGSAT (6 letters). NAGS is a verb meaning to scold or criticize someone in an annoying way. PESTERS is a verb meaning to annoy someone with persistent and unwanted attention. EATSAT is a combination of the words 'EAT' and 'SAT, ' which together mean to remain in a certain place for a long period of time. Finally, NAGSAT is a combination of the words 'NAG' and 'SAT, ' which together mean to persistently scold or criticize someone in an annoying way.