I have had exactly the same problem. There doesn't seem to be any fix for this. Basically you need to have the Slingbox where someone can unplug it for you each day or two as required. This obviously is impossible if you are on holiday or working away from home. My retailer swapped my first Slingbox Solo for me for a new one but to be honest with you, I never use it now. I found the hassle of not knowing if it would work when you wanted to use it just wasn't worth it. I think it's fine for sending TV around the home network but just not a robust enough solution to be relied on when away from home for any period.
I determined that I had a heat sensitive circuit causing the network light to disconnect. By cooling the solo down with an inexpensive laptop cooler (you may also need a USB AC adaptor), I have eliminated the disconnect problem. One way to test is to cool the solo for 15 minutes in the refrig and then place in a location where the ventilation is good. If the unit does not disconnect for 48 hours then you may have isolated the problem.
What I understand from your post, is that your Slingbox Solo is losing the connection from time to time.
In this case, what I would recommend, is to check the following link which provides some troubleshooting steps for that type of issues.