I've seen this issue happen repeatedly on some machines. The root cause seemed to be in the bowels of the Java version / installation on the client. The solution which I found to work most reliably was to uninstall Java completely on the client and then launch a CiscoWorks applet like Topology Services.
At that point, LMS will redirect you to the Java binaries that are provided on the server where they will be downloaded and installable on your client. That particular binary package has all of the optional Java bits to insure optimum compatibility with LMS. Subsequent client Java upgrades to the more current version did not seem to affect the interoperability following that procedure.
I would agree with Marvin's second paragraph. I have been regularly upgrading my Java 6 install on my workstation, currently at version 6 update 38, primarily for stability and security fixes. I started with the built-in Java that LMS wants to install, then have continually upgraded as newer Java versions have come out, mainly to see if each update fixes ongoing issues I'm seeing. Unfortunately, I have not seen any improvement in functionality or stability, but I haven't seen any negative issues either.
I encountered this problem. Repeated attempts uninstall and reinstall Java did not help.
This is a single application (LMS) in a controlled environment, I started checking backwards on changes. The last change was Microsoft EMET, recommended by CISecurity.
22.214.171.124 (L1) Set 'Default Protections for Recommended Software' to 'Enabled' (Scored) Profile Applicability: Level 1 - Domain Controller Level 1 - Member Server Description: This settings determine if recommended EMET mitigations are applied to WordPad, applications that are part of the Microsoft Office suite, Adobe Acrobat, Adobe Reader, and Oracle Java. The recommended state for this setting is: Enabled.
Using GPEDIT.MSC, Set the following to disable.
Computer Configuration\Policies\Administrative Templates\Windows Components\EMET\Default Protections for Recommended Software