Though it’s quick and easy to request a ‘Blue Verification Badge', it rarely comes through. It is recommended to know the criteria and the right method to apply for a badge.
The blue checkmark is granted by the Facebook team only after considering an application that is notable i.e. backed with press coverages and applied via the right agency partner.
Yes, your verification badge will be permanent. However, at any point, if Facebook discovers any activity that goes against their policies, they take down the verification badge.