When submitting a form in BF 1.8.1 build 809 on Joomla 2.5.8 I got the message Could not instantiate mail function. The form was submitted to the database, the submitter of the form received a copy of the form but admins did not get an email of the submitted form.
The solution for me was to switch off Mailback as sender on the email element. (I wanted to reply direct to the submitter of the form but now I will not be able to do that!) A small price to pay in order to get the form going to admins.
So, If you want the form to go to admins, un-tick the box on the email element in the form that says, Mailback as sender. Your form will not be considered as PHISING by your web host !
That has taken a long time for me to resolve this issue. I hope it helps others.