Question: We're having to reboot frequently (once per day) because we're getting a 9001 error from SQL Server on our VPS.
Rebooting seems to resolve the problem, and we're discussing it with our provider.

Q: Does everyone lose their session scope when we reboot?

Answer: 
Yes, assuming that you are using ColdFusion's session scope in memory. All memory is cleared when the server is rebooted. Sessions could persist if you are using a database or some other external source.

And for what its worth, the application scope and server scope are also cleared.
Yes. Sessions are server side variables. I tested it just now.