iCloud calendar not sending invites
Found this @ http://productforums.google.com/forum/#!topic/calendar/gtpX0F7kgKI

For what it's worth, I started having a similar issue recently and came across this thread while researching the solution. My wife has an iPhone, I'm Android, and she routinely sends calendar invites to me. We just realized that I've recently stopped getting those invites to my Gmail account, even though she's still adding me the same way she always has. It turns out that since my iCloud account is setup with my Gmail address, iCloud has started to "intercept" those invites from her iPhone. Instead of going to my email account, they're being automatically added to my iCalendar. This can be disabled by:


Logging in at https://www.icloud.com
Go to Calendar -> (Cog) -> Preference -> Advanced 
Beside "Invitations" select Email To  (Use this option if your primary calendar is not iCloud).


This may solve your problem if:


Someone with an iDevice is sending your the invite.
You have an iCloud account.