If the software indicates there is a connection problem, then you need to check the network you're connected to because the Internet might not work correctly. To study the behavior of the Internet connection, simply connect to other network and load a Snapchat story. If the network connection and the reception is good, then you'll see an improvement, otherwise re-install the Snapchat application and use the same details to log-in because this could also be a problem of the software.