Every time the MacBook Air comes out of sleep, the Skype window gets hanged.

Hello gauriamin,

Thank you for posting to Apple Support Communities.

We understand that you're having an issue with an app on your Mac. We'd like to help.

To begin with, let's have you restart your Mac to test if the issue continues: Shut down or restart your Mac - Apple Support

Then, let's have you check to be sure that your Mac is up-to-date. Here is how you can do this: Keep your Mac up to date - Apple Support

If the issue continues, you can then try removing the app to then reinstall it:

Install and uninstall apps from the internet or a disc on Mac - Apple Support

Install purchases from the App Store on Mac - Apple Support

If the issue still persists, we then recommend contacting the developer of the app for additional help: How to contact an app developer - Apple Support

We trust that helps. Let us know if you have any questions.

Take care.