After I upgraded from version 3.15 to 3.16, I can't connect to the server -- TSS handshake failure. I can connect to it via another email program.
What's TSS? Do you mean TLS? If so, this is possibly a duplicate of Bug 3941. If you're using OpenSUSE, try switching your packages to the versions in the server:/mail YaST repository.
Can you say what server this is? With 3.16.0 we upgraded GnuTLS (the library responsible for TLS connections from version 3.5.2 to 3.5.9, so perhaps the server is too old and uses TLS settings which are considered insecure by this newer version.