OK. I cannot reproduce the problem from our Android mobile devices, but I sort of did with our iPod Touch after installing the Skype for iPhone app.
Using that device, the first time I send a chat message it does not generate the chat received event, but the second one always worked immediately after. I tried this about 15 times.
As well, even once working, if I waited 5 minutes without sending anything, and then sent another IM, again the first attempt does not generate the chat received event right away until I sent the second IM. The second IM always worked for me.
That's all I can report so far. I'll pass the info on to James, but I doubt there's anything that can be done on the VC side of things.
[Update: "upgrading" to the new versions of Skype mobile on Android devices causes the same issue as with the iOs version. Older versions work fine--it is only the post December 2013 versions of the Skype apps that don't trigger an event with the first IM sent. The 2nd IM is received properly.]