Have you verified that there is plenty of air circulation around your SB? I find that mine run "hot" and I have insured that there is at least a foot of clear air above it, and I have added extra rubber "feet" to its bottom to raise that bottom at least one inch above the flat surface beneath it. If it is "overheating", that might be triggering the loss of internet connection.
Unplugging and plugging in the power supply might then reset the system -- but this could also indicate that your power supply is failing to deliver the near-4-amps continuous current necessary to power the device while slinging. So you might consider whether a replacement for a failing power supply is needed. Since my SB is no longer under warranty (which could provide a free power supply replacement), I purchased a comparable replacement (rated at 5 volts, 4 amps) from bgmicro.com
Another possibility is that your Internet Service Provider is throttling your upload connection if the data transfer exceeds some unknown-to-me but perhaps specified-by-your-ISP limit in megabytes-per-hour of allowable uploads. You might check with them if they have any such limitations, as the amount of data transferred will be more than a gigabyte per hour if you are streaming HD resolution video.