Another way to get the missing requests is to open Skype → Tools → Settings → Privacy, change any option (for example, enable/disable “Accept Skype browser cookies”) and click “Save”. After a few seconds, you will receive all contact requests. About this method told me Artemy (a reader of Russian side of the blog).
It seems developers are testing a fix for contact requests issue. According to my tests in the insider build 188.8.131.52 contacts requests works properly and I receive them as expected. You can download the insider installer at this URL https://aka.ms/skypeinsiderregister (please let me know if it works for you too).
Apropos, if you want to help developers to improve Skype, you may consider to join the Skype Insider Program here http://community.skype.com/t5/News-and-Announcements/Launching-the-Skype-Insider-Program/ba-p/4519332
Chronicle of events:
The first report about this issue on the official forum
Insider build fixes the issue
Bugfix has been deployed to all affected users