This right here actually proves the issues is not on Blizzard’s end, but rather something specific to you. If two people are using the same connection, and one stays connected and the other doesn’t, it absolutely means the issue is happening at a point outside of Blizzard’s control.
It could be a modem issue prioritizing one PC over the other, or it could be outdated drivers. It could also be failing hardware.
You’ll want to start the troubleshooting process as described in the following link: