pester power

noun

the ability possessed by a child to nag a parent relentlessly until the parent succumbs and agrees to the child's request

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012