I understand that you are having some issues with your Slingbox Classic since its connection speed dropped down to less than 200kbps.
Most of the times, this issue is related to a slow connection speed. If the Slingbox does not get the required connection speed, it will not work in a proper way. The following link will provide you with further information.
If your Slingbox has a good connection speed at home, you'll need to check if your current network meets the requirements for a good streaming signal. Among other things, check the available bandwidth (since other users might be using the same network at certain moments).