ASSP uses the perl module IO::Socket::SSL to secure smtp connections . cPanel updates daily perl modules and perl module IO::Socket::SSL too .
Latest IO::Socket::SSL version 1.70 will crash your ASSP (and your EXIM too). To avoid this problem please be sure to update your ASSP WHM to version 6.1.5 or above and your ASSP Deluxe to version 5.3.0 or above ; this versions will force the usage of IO::Socket::SSL version 1.68 .

If your ASSP is already crashing because you already have  IO::Socket::SSL version 1.70 , upgrade your ASSP WHM to version 6.1.5 or above and your ASSP Deluxe to version 5.3.0 or above ; after this step open your ASSP WHM interface and click "Update ASSP Perl modules" .

Your IO::Socket::SSL will be downgraded to 1.68 ; after this step you should be able to START your ASSP and it should work correctly .