Unreliable call notifications on Lumia 920 Windows Phone 8

Question

[Topic title updated by moderator to better reflect the discussion topic]
My wife and I both own the Lumia 920 with the latest Windows Phone 8 update (GDR2/Lumia Amber). We have installed Skype on each handset. We are signed into the app and into our Live accounts. I used her phone and Skyped my phone. Nothing happened. Though her Skype app showed my phone to be "ringing," my phone in fact never gave any indication that a call was trying to come in. There was also no notification on the lockscreen, though I enabled that feature on my phone's settings.
I went into the Skype app and looked under its settings, but all I find are toggles to turn on Skype and Messenger messages, both of which are on. I know that I'm missing something. I checked Background Tasks on the handset. Skype doesn't show up on the list of blocked apps. But neither does it show up as "allowed." When I go into Background Tasks > Advanced, there is a list of grayed-out items that I "may not be able to block," and Skype is on that list. But I can find no option to manually permit it.
How do I know when someone is Skyping me?
Thanks!

Answer 1

It's been over a month since my first post and providing the Skype team with details for them to troubleshoot, still no word from them. I have almost all the issues that you would find online about Skype and nothing they said is fixed works for me. I have since tested on my iPad 2 (iOS 7) as well, same story and having multiple devices made it even worse. I don't get sound when text notifications arrive on my iPad, just on-screen alerts (yes, Skype notifications have been set to play sound). Calls only show up as missed calls after the fact, just like my WP8. Skype was unresponsive when I tried to pick up a text notification on the iPad and I had to switch over to my WP8, just to have my first failed reply using the iPad pop up the next day on my PC. What's even funnier was the other side received this "first" response 5 or 6 hours before I saw it on my side and his response to that didn't get to me until 7 hours later when the real conversation concluded the night before. The multiple device sync they said they fixed back in the Feb release isn't working either. I would be texting away on the iPad and my phone sitting right next to me would be pinging away with notifications. So much for only sending notifications to the active device. Maybe they're pinging my phone to compensate for the soundless iOS? Even something simple as emoticons is messed up. I've received them as code on my PC from someone texting me from another Skype account, they've turned into little squares or code if I view the conversation on a different device from the one I used to send them originally. Profile pics of contacts appear and disappear at random. Even what you think is the most stable and functional PC version is crapping out. Statuses of my contacts are rarely current and you need to log off and log back on to trigger it to refresh. And that doesn't work 100% of the time. Renaming contacts on the PC does nothing when you view it on other devices. So my contacts who have mutliple accounts show up with the exact same name multiple times on my WP8 and iPad. I have to go into the contact details in order to tell which one is personal and which one is work. I don't think you can make it this bad if you intentionally tried. They have essentially killed two great products with one merger and pissed off both loyal Messenger and Skype users. If I didn't have contacts on Lync, which only Skype can reach when you don't have Lync at home, I would have been so gone.