1) Assertive 2) Beseeching 3) Continual 4) Demanding 5) Demanding attention 6) Earnest 7) Hard to brush off 8) Hard to deny 9) Importunate 10) Not giving up on an argument 11) Not taking no for an answer 12) Persistent 13) Persistently continual 14) Persuasive 15) Pertinacious 16) Pleading 17) Repetitive Found on https://www.crosswordclues.com/clue/insistent
In·sist'ent adjective [ Latin insistens , -entis , present participle of insistere .] 1. Standing or resting on something; as, an insistent wall. Sir H. Wotton. 2. Insisting; persistent; persevering. 3. (Zoology) See Incumbent Found on http://www.encyclo.co.uk/webster/I/69
earnest or emphatic in dwelling upon, maintaining, or demanding something; persistent; pertinacious. · compelling attention or notice: an insistent tone. Found on https://www.infoplease.com/dictionary/insistent