Intermittent failure in AutomaticIndexStatisticsTest.testShutdownWhileScanningThenDelete on Windows

The test AutomaticIndexStatisticsTest.testShutdownWhileScanningThenDelete fails intermittently on Windows platforms because the test is unable to delete a database directory.
Even after several retries and sleeps (the formula should be (attempt -1) * 2000, resulting in a total sleep time of 12 seconds), the conglomerate system\singleUse\copyShutdown\seg0\c481.dat cannot be deleted.

For instance from http://dbtg.foundry.sun.com/derby/test/Daily/jvm1.6/testing/testlog/w2003/1078855-suitesAll_diff.txt :
(truncated paths)
testShutdownWhileScanningThenDelete <assertDirectoryDeleted> attempt 1 left 3 files/dirs behind: 0=system\singleUse\copyShutdown\seg0\c481.dat 1=system\singleUse\copyShutdown\seg0 2=system\singleUse\copyShutdown
<assertDirectoryDeleted> attempt 2 left 3 files/dirs behind: 0=system\singleUse\copyShutdown\seg0\c481.dat 1=system\singleUse\copyShutdown\seg0 2=system\singleUse\copyShutdown
<assertDirectoryDeleted> attempt 3 left 3 files/dirs behind: 0=system\singleUse\copyShutdown\seg0\c481.dat 1=system\singleUse\copyShutdown\seg0 2=system\singleUse\copyShutdown
<assertDirectoryDeleted> attempt 4 left 3 files/dirs behind: 0=system\singleUse\copyShutdown\seg0\c481.dat 1=system\singleUse\copyShutdown\seg0 2=system\singleUse\copyShutdown
used 205814 ms F.

Maybe the database isn't shut down, or some specific timing of events causes a file to be reopened when it shouldn't have been (i.e. after the database shutdown has been initiated).