How to make "Permanently store this exception" checkbox active?
The option which disables the ability to store security exceptions appears to be Never remember history. You can find it in Options->Privacy->History. Once you switch it to Remember history and restart Firefox, you can permanently store the security exception. If you then switch that option back, the exception will remain stored, so you can enable this feature back after adding the exception.
Confirmed answer from @sdanna. I had to allow "Remember History" temporarily, set the permanent checkbox on my desired site exceptions one by one and then switch it back to "Use Custom Settings." Worked perfectly after that.