Thank you for posting on the answer forum. It sounds like the ISP is bottle necking the speed between those hours. The only reason I think that it is the ISP and not the Slingbox is because all hours of the day it works except between 8PM and 10 PM. I have an article I would like you to look over and you should contact your ISP and see if anyone else is having the Same issue between these hours.
Hope this helps,
Sling Moderation Team
Just to add a suggestion which might help with the Pro-HD - try setting the Slingbox to use port 443 instead of 5001 (which is likely what it is using).
It's not impossible that the ISP is throttling certain ports only, if FTP is unaffected between these times.
If it makes a difference you unfortunately wouldn't be able to use the same trick for the SB 350 as you can't change the port used with that one.