That message is a result of your server throwing a 503 error and the WordPress Heartbeat API catching that error. See https://core.trac.wordpress.org/ticket/25660 for the background on the fix that WordPress introduced to save offline edits.
Things to check on your computer are if WAMP is actually running when you’re getting this message (check the status icon in the system tray). You should also check to make sure no other programs are trying to take over the port WAMP uses. Reports of Skype and TeamViewer taking control of ports 80 & 443 abound, as well as fixes for each of them.
If you haven’t checked out the WAMP forums, here’s a page that outlines the debugging steps for the 503 server error, and fixes for Skype and TeamViewer: http://forum.wampserver.com/read.php?2,115474,115576.