Its not obsolete, it may be considered poncey by some. Then again I know people who think words like 'defiance' or 'triumphant' are 'gay'. Its a perfectly good word and still in common usage in Ireland and Britain. If its in use, its not obsolete. Random example from RTE News (an internet story mind you)
http://www.rte.ie/news/2011/1227/twitter.html
this google news search for 2010-2011 produced 9,330 instances of 'erstwhile' from all over the world.
It sometimes implies a slightly comic tone. Also it might imply that the subject might return - ie no longer be "former". Ueser jimsun (February 2007)
Are you certain this word is obsolete in the adverbial usage? I see it in contemporary writing with some frequency. Perhaps, then, it should be considered literary?
I say, chaps, here's a dictionary that doesn't treat us all like fucking plebs. No need for a definition of "erstwhile" is there? Any more than for table or bumboy, is there? Should be more of it. Well done sir, have a glass of port on us.