Do you still see the post-processing options? If not, you have accidentally installed the Core version on top of the Professional. Install the Professional version on top to fix that.
If you still see the post-processing options, has any other option been modified (other than file, folder and database filters)? If it has, something changed in the cryptography setup. This can mean that either the server key file was accidentally deleted (e.g. the host deleted it without a warning because they mistook the base64 encoded cryptographic key for malicious content - it wouldn't be the first time) or something changed in the server configuration which affected cryptography. In this case setting up the backups is, unfortunately, the only option.
Please note that since several months ago -almost a year now- we have switched from using the obsolete PHP mcrypt module to the PHP OpenSSL module for handling cryptography. This shouldn't be a problem unless you have a server whose PHP OpenSSL module is compiled against an ancient OpenSSL library that doesn't properly support AES-128.x Again, in this case your only option is to set up the backup again.
Finally let me note that the settings storage is part of Akeeba Engine, the backup engine which is common across all of our backup products (Solo, Backup for Joomla! and Backup for WordPress). On top of that, Backup for WordPress and Solo are actually the same application with a different GUI wrapper (WordPress plugin vs none) and a different Platform component (integration with the lower level system, WordPress vs direct PHP). It doesn't make sense that encryption works on two but on the third. If I were to guess I'd think that the WordPress sites are on a different server setup than the rest of your sites (Joomla! and those backed up by Solo).
Nicholas K. Dionysopoulos
Lead Developer and Director