Hardware issues

Wi-Fi connection: If you are using a Wi-Fi connection, try connecting your system to the router via a network cable. If this solves your problem then consider replacing or up-grading your Wi-Fi router or adapter. Also your security settings may be set to not allow full bandwidth usage which will limit the amount of data that can be sent or received at one time which will cause connectivity issues.

CPU temperature: Check your CPU temperature with speedfan. It is a freeware program that monitors voltages, fan speeds and temperatures in computers with hardware monitoring chips. Different CPUs run at different temperatures and have different heat tolerances before performance becomes impaired. Consult the manufacturer websites (Intel, AMD) or see here for more information.

Make sure fans are working and remove dust and dirt from fans and air vents.

Substitution: Try Skype with a different set of hardware (another computer, a friends house, etc.) to see if the problem persists. Also, you can test the hardware with another un-related application (such as Yahoo, GoogleTalk, etc.) to see if you have similar issues.

Power: If you are using a USB device, make sure the USB port provides sufficient power for your device. This would be an issue especially if you are using a USB hub and have multiple devices connected to the hub.

Skype issues

Rarely, Skype may have software issues which bring down portions of the network. The outages are normally announced in the Skype website.

If your issue is Skype account related, you need to contact Skype support team for resolution. Read this article on how to get support from Skype.

Good luck.