The download counter stopped on Tuesday March 17 at the number of 1,168,075,188 downloads.
Then on Friday 27, it suddenly began to count again, but starting around 500 million downloads, and some hours later it jumped up to about 627 million. It keeps counting, but it seems Skype lost half of its historical downloads. I guess this is a bug, and that the engineers are still trying to solve it.
[EDITED AT 18h25 GMT+1] Some minutes before i published this post the download counter got stuck again at 633,382,728 downloads.
What caught my attention however is the download speed! It has risen to 1200 downloads per minute, while it was less than 600 per minute before the “counter crash”. Impressive acceleration, and I made some speculations in the past about the reasons, without being sure.
[EDITED at 18h50 GMT+1]