Just wanted to tack onto this thread that the above message may be seen when accessing a server which implements (perhaps after an upgrade TLS extensions which are not supported by the older SSL implementation on Palm/HP webOS devices (I can't speak to such support under Open webOS or LG webOS).
I upgraded my mail server from CommuniGate Pro 5.2.18 to 5.4.10 this afternoon. Immediately, my Pre3 and TouchPad complained that they couldn't connect to the server (configured for IMAP on port 143 with TLS). I use a self-signed cert on the server, and this did not change. Nevertheless, I deleted the cert from both devices and added it back. Still, I got the above, with the details provided as:
In the browser, attempting to connect to webmail or the admin interface, the TouchPad just threw (an unhelpful) "Unable to connect to server" popup.
Unable to sign in; unable to validate incoming mail server settings. Check the settings and try again.; Requested encryption not supported by server. Error code 9820: Non-specific SSL protocol error -- src/network/SocketConnection.cpp:168
CommuniGate's support knowledgebase came to the rescue with a startup parameter for the server, explained as:
Sure enough, once I added this and restarted the daemon on the server, I was able to establish TLS and SSL connections, and the web interfaces came right up.
This one has been added as the workaround for problems accepting TLS connection requests from clients that used older versions og OpenSSL libraries and advertize support for some TLS extensions which are not really supported. Examples of this are financial institutions unable to send mail to your CGP server. Connection is made but TLS fails to negotiate. More on what the TLS Extensions are (and in turn what is disabled when you use the above parameter) can be found here: http://www.ietf.org/rfc/rfc3546.txt
So, the point is that sometimes it may be something on the server side. Obviously, I'm in a better position than most in this regard, as I run my own mail and web servers and can troubleshoot from both sides, but the moral here is that should something like this just come about all of a sudden, it might be worth at least asking the provider if there has been a change to the security protocols (not just the certs!) on the server.