This happens sometime, not always.
The caller heard one rang then the call went direct to voice mail.
I was in the full bar services area and can still receive email and IM via LTE, but I did not see any missed call notification nor incoming calls.
This happenes to my AT&T iPhone 5.
The Do Not Disturb and Airplane Mode are both off
How can I fix this?
Go to settings/general/reset/reset network settings. That should do it.
Same here: iPhone 5, iOS 6.1, carrier Swisscom: Missing calls (diverted straight to voicemail) when LTE is enabled. The issue disappears when I switch LTE off. The failure rate is maybe 50% with LTE on (i.e. some calls do come through).