Quite easily obtained from the ESPN.com schedules (same source I use for the when-the-Nth-win-was-notched posts, thanks to their cumulative win-loss numbers by each result).
Cumulative dates on which the Nationals registered their 4th loss, each season:
2007 - 6th April (5th match of season)
2011 - 6th April (5th match)
2008 - 6th April (7th match)
2006 - 9th April (6th match)
2009 - 10th April (4th match)
2005 - 11th April (7th match)
2010 - 12th April (7th match)
2012 - 19th April (14th match)
Thanks for that Chelsea. When I asked the question, this is kind of the results I expected. The 2012 stat looks real good in the grouping.
And here I thought you had all this stuff in your mind.