You may have started Evolution with the --offline commandline option to enforce offline mode.

If this is not the case and Evolution normally works but has suddenly stopped connecting to your mail accounts, you may have unintentionally clicked on the connection icon in the lower left corner. When connected, the icon resembles a pair of sockets joined together. If the sockets are open, there is no connection to your mail accounts (and the Send/Receive button is grayed out). Click on the icon to change its state.

If the problem persists and you are sure you have not clicked the icon, but you can still reach the network from other apps on your system (browsers, FTP, SSH, ping etc.) it may be that your network connection is not properly configured. For more information please take a look at the Desktop help or seek help from your distribution support forums, mailing lists etc.