Add me to the list of dropouts as well.  I do not power down my BDP-1 and it will happen the next day when I go to use it.  As with others, it happens on the first track I play.  In my case, I can hear the audio for a split second, then I get silence for a second, then the sound comes back.  If I skip back it works fine.  The hard drive is a western digital my passport essential 2 tb although it also occurred with the 1 tb version of the same drive.  My BDP-1 is connected directly to a Classe SSP-800.
Great description of the issue.  First track of the day: 2 to 4 seconds of sound, silence, then sound.  When I hit back, it plays straight through.  This issue occurs regularly enough, that it got me into the habit of hitting play, waiting 3 or 4 seconds, then hitting back, to listen to the whole song uninterrupted. 
I just powered up my BDP-2 to confirm it.  Like clockwork, there was sound, silence, then sound.
In my opinion, it has nothing to do with the type of drive or the track that is being played.  I experience this issue with flash drives, SSD attached via USB dongle, streaming radio, and with internal SSD inside the BDP-2.