Hi SagerCat,
As far as I know, the impact of the leap day issue is no longer there. Do you still have that recycling problem with your deployments? There's something I think you can try :
1. If you have configured remote desktop connection, logon to check the event logs and C:\logs\** files. You might find some footprints of the restarts.
2. Did you try re-imaging them? Some of my customers were able to solve their problem by doing that.
3. If the problem is still going on, I really suggest you to raise a service ticket at
http://www.windowsazure.com/en-us/support/contact/ . You will leave the deployments running, provide your subscritpion ID, deployment ID, the symptom and the accurate time (with timezone)
. people will help you check both your VM and the hosting environment.
-Emma