You might have an issue with your internet connection.If you are not signed in or the app isn't running, you may not receive incoming message notifications. Make sure you are signed into Skype and it's running on your device.We're always making improvements, so be sure to keep Skype updated for the best performance. The site will tell you if there are any reported issues. Having problems sending or receiving messages in your Skype chats? The following tips should help.