While Skype has not provided an official solution for this problem, there are several things you can try. Make sure you are using the latest version of Skype by clicking 'Help' and then 'Check for Updates' from within Skype. If that does not solve the problem, try closing Skype and turning off Compatibility Mode if necessary. Right-click the Skype icon, click 'Properties' and then navigate to the 'Compatibility' tab to turn off this mode. Simply testing your internet connection through Skype may be enough to resolve the issue. To do this, click the 'Check Settings' button in Skype and then select the 'Connection' tab. Click 'Test Now.'
If nothing works, you may need to inform your contacts of the issue and call them back rather than accepting their calls. You may find that you miss your chance to answer some calls because you are not receiving the necessary notifications. To resolve this, open Skype and sign in.
Click 'Tools' at the top and then 'Options' from the list that appears. This opens a new window, in which you should click 'Notifications.' Click 'Sounds' within this section. This brings up a list of all the times when Skype can notify you of an event with a specific sound. Click 'Enable all sounds,' and then click 'Save.'
Select a recipient's name from the left-hand side of the Skype window, then click the video camera or telephone icon in the top-right side of the window. This will begin calling the recipient. You can share your screen while on audio calls and while on video calls. To open the actual Skype folder, right-click the application icon and click 'Show Package Contents.' This opens up the application and makes it possible for you to view the folder contents.
You should now hear a sound when someone calls you on Skype, allowing you to answer rather than miss the call.