Last race that I completely missed was Britain 2003, as I was on holiday :(
Last qualifying session that I did not see at all was Japan 2004 (for obvious reasons). Plus of course the Sunday part of qualifying in the early 2005 races.
Last race that I did not watch full coverage of (only highlights) was USA 2007.
Last race that I did not watch live was Japan 2008 (I watched the re-run, which had an ineptly timed ad break despite not being live). I can’t remember if I watched qualifying for China 2008 live, but I did get up early for the race :(