If it's only happening to some of the people, that would seem to point to a problem other than Blogger not sending the emails out. Have
Have the individuals who didn't get the email check their spam/junk folders in case it landed there by mistake. You
You could also have them add your email address (if Blogger uses it as the "from" address) to their address books so future emails won't get filtered.
If you have a second/alternate email address, have Blogger send an invite to that email so you can see what the invite looks like. If
If you don't have one, set up a free temporary email account with Forward CatForward Cat and send the invite there; it will be forwarded to your real email address.