Does it happen at a certain level, some amount of time spent playing, or are they handed out ad-hoc?
I've made it to level 3 without acquiring an invite to give. I'll let you know if and when I do.
By the way, the ingress.com/intel webapp is way faster than the ingress scanner app for just checking if you have any invites or not.
I believe the invites were given out ad-hoc. Once all level 7+ got 3 invites to give out. Recently all level 2+ (maybe 1+) got 5 invites to give out.