Here using a full join where both sides are null we can get all our new or old clients and depending on where the nulls are can assign whether they were a new client or lost client.

DECLARE @StartMonth DATETIME = (SELECT DATEADD(MM,DATEDIFF(MM,0,MIN(SaleDate)) + 1,0) FROM #Sales)

DECLARE @EndMonth DATETIME = (SELECT DATEADD(MM,DATEDIFF(MM,0,MAX(SaleDate)),0) FROM #Sales)

SELECT CASE WHEN s2.ClientID IS NULL THEN 'NewClient' ELSE 'LostClient' END AS ClientAction,

RIGHT(CONVERT(VARCHAR, ISNULL(s1.SaleDate, DATEADD(M,1,s2.SaleDate)), 106), 8) AS SaleDate,

ISNULL(s1.ClientID, s2.ClientID) AS ClientID

FROM #Sales s1

FULL JOIN #Sales s2

ON s1.ClientID = s2.ClientID

AND MONTH(s1.SaleDate) = MONTH(s2.SaleDate) + 1

WHERE (s1.ClientID IS NULL

OR s2.ClientID IS NULL)

AND (s2.SaleDate < @EndMonth

OR s1.SaleDate > @StartMonth)

ORDER BY ISNULL(s1.SaleDate, DATEADD(M,1,s2.SaleDate)), ISNULL(s1.ClientID, s2.ClientID)

EDIT: Fixed code to eliminate the fact that all clients in january were new (no DEC 2011 DATA) and all clients in Jun were lost (no data for JUN 2012).

this should work when you add in more months as i take the max and min from the table.