How can I get the Steam client to reestablish its connection?

I've seen this happen often when I put my laptop into sleep mode, and then later start using it again. Sometimes Steam will manage to reconnect itself. When it doesn't, I find I have to close down all of Steam, including its background tasks and then restart the Steam client (which restarts all the background tasks). This always works for me.

Hello fellow MacBook Pro user! I tried going in sleep mode with Steam online on my MBP with Mac OS 10.7.4 and newest Steam and nothing bad, like losing connection after, happened.

I can reconnect by opening View Friends List and then Log In button.

IMHO that this sleeping issue might be connected with your Energy Saver preference panel not Steam.

To fix same problem on linux, you need to wrap NetworkManager library (nm-utils.so.2 and nm-glib.so.4) like http://pastebin.com/4WFMbXEc. There is a bug that locks steam while libnm is trying to connect to NetworkManager via dbus when NetworkManager is not installed.