On 10 October 2016, Mark Watkins reported that 1 e3 had finally been proved to win for White under both International rules (the original rules whereby stalemate is a win for the player stalemated) and Free Internet Chess Server rules (stalemate is a win for the player having fewer men remaining on the board). Details can be found on his web site http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/. In particular, he has written a draft report
http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/LCsolved.pdf
and there is also currently a browsable version of the solution
http://magma.maths.usyd.edu.au/~watkins/LOSING_CHESS/browse.html
though he doesn't know how long he will be able to host this.
The proof tree contains a little over 929 million nodes, and occupies approximately 7.1GB of storage. A further 400MB are needed for four-man tablebases, each line being followed down either to a position where White to play has no move, both FICS and International rules being catered for in the event of stalemate, or to a position with only four men.
Approximately half of the proof tree deals with 1...b6, a further quarter with 1...c5, and the remaining quarter with everything else.