That assumption (about JSSE for Sun's JDK) should be correct.
Can you try smtps instead, e.g.
Transport trans = theSession.getTransport("smtps");
You probably also need to change your resource's smtp properties to use "smpts" as well.
When you start w/ smtp, it is probably using TLS to switch a regular socket to SSL and something is falling down somewhere. (Debugging the connection code might indicate the responsible party and the reason for the socket failure, but I have run out of speculative ideas at this point). Using smtps directly may bypass all this trouble.
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