Hi Serge,
There isn't a way at this time to figure out exactly why an invite failed, but that's a good idea, we'll take that into consideration.
The main reasons user's may fail to be sent an invite are:
1. They already have the app (but you knew this already)
2. The user is blocking app invites or the app specifically, or has some other permission setting that is preventing messages
3. The users aren't friends
That's about it, you're probably running up against #2 more than likely assuming you take care of #1.
Chad