It seems SingleInstanceService for applets which allows apps to register themselves as singletons si not working properly or there are some issues with implementation of SingleInstanceListener witin applet environemnt.
Load following applet inside the browser
If you notice log as below then bug is reproduced:

Applet: JNLPSingleInstanceService1 [480x120]
getDocumentBase(): http://nicole1.sfbay.sun.com:8080/plugin_tests/JNLPSupport/applets/AppletBasics/JNLPSingleInstanceService1-jnlp-applet-rel.html
getCodeBase()    : http://nicole1.sfbay.sun.com:8080/plugin_tests/JNLPSupport/applets/AppletBasics/codebasedir/
getAppletInfo()  : null
isActive()       : true
java properties  :
         vendor           : Sun Microsystems Inc.
         version product  : 1.6.0_10
         version platform : 1.6
         max heap size    : 66650112

10: waiting [activations: 0, expected: 2]
9: waiting [activations: 0, expected: 2]
8: waiting [activations: 0, expected: 2]
7: waiting [activations: 0, expected: 2]
6: waiting [activations: 0, expected: 2]
5: waiting [activations: 0, expected: 2]
4: waiting [activations: 0, expected: 2]
3: waiting [activations: 0, expected: 2]
2: waiting [activations: 0, expected: 2]
1: waiting [activations: 0, expected: 2]
         activations: 0, unequal expected: 2 - failed
TestResult failed