I have been experiencing same issue.
It tries to update, sometimes the error shows straight after clicking update, sometimes after it gets to installing stage...
Code:
org.jdownloader.update.SelfUpdateException: Unexpected Selftest Result: FAILED org.jdownloader.update.lastchance.FailedException: org.appwork.updatesys.client.defaultimpl.http.NoConnectionException: Could not Connect to http://update.appwork.org/jcgi/lastchance?app=JD&pkh=12f1848a883e733ed40fffff0dae2f35&jh=435d2eac5f2dee7000443eb4df4ae4ae&rev=-1&srev=-1&urev=-1&surev=-1&rt=ST
at org.jdownloader.update.SelfUpdateClient.validateSelfTestFile(SelfUpdateClient.java:488)
at org.jdownloader.update.SelfUpdateClient.finishSelfUpdate(SelfUpdateClient.java:320)
at org.jdownloader.update.UpdateManager.runFinishSelfUpdate(UpdateManager.java:940)
at org.jdownloader.update.DefaultCallbackHandler.onResults(DefaultCallbackHandler.java:369)
at org.jdownloader.update.UpdateManager.runUpdateLoop(UpdateManager.java:1299)
at org.jdownloader.update.UpdateManager$6.run(UpdateManager.java:378)
at java.lang.Thread.run(Unknown Source)
In about JD: