We went direct to the banks ourselves earlier this year for AIP. Our approval in principle from BOI was for 3 months (then we'd need updated payslips and bank statements to renew it). They said it used to be longer, but nowadays they like to revisit things more often. Halifax mentioned 6 months I think, so it varies from place to place.
Whichever bank your approval is with, just ring their head mortgage office and ask them how long it lasts.
Just because you go through a broker does not mean you can't ask the Bank questions directly. If the approval runs out, you can just resupply the few updated documents.
Make sure and keep any bank statements, payslips etc that arrive from now on in a separate envelope somewhere safe.
The broker doesn't get his money until you draw down the mortgage so that's why he's applying pressure. His problem, not yours.