Can I get steam to reconnect without restarting?
Solution 1:
Sadly, I don't think there is another solution for on-the-go options. Steam actually should really reconnect itself when it's possible, but there is no way to force the process apart from restarting Steam. Losing connection has happened to me and letting it reconnect on itself worked for me. In my opinion you should focus on solving the problem, not working around it.
You could try reinstalling Steam on your rig, as mentioned in the comments, maybe something corrupted Steam files? You didn't mention in your question whether you have already tried this.
Some more insights you might want to consider:
• provide information on what OS this happens - maybe it's OS relevant?
• do you use any firewall/antivirus software? Check its settings, look for blocked ports and cross-reference them online to see what might be used by Steam, look in blocked files/quarantine if something from Steam wasn't blocked either
• does this happen when you do any specific action on randomly?
• does Steam launch in this state or does it happen some time after launching?