1. Continual and persistent demands
   "His insisting on perfection made him difficult to work with";
   - insistence

1. Be emphatic or resolute and refuse to budge
   "I must insist!";
   - take a firm stand
    
2. Postulate positively and assertively
   "He insisted on his innocence";
   - assert
    
3. Beg persistently and urgently
   "She insisted on speaking to the manager";
   - importune

Type of: beg, cerebrate, cogitate, demand, implore, posit, postulate, pray, think