Verified that the iOS deviceToken is identical for both LTE and WiFi.
This issue may occur not because of any inherent difference between LTE/3G/WiFi, but because of switching between these modes, which may result in a short-term mismatch with the adaptive heartbeat. My testing today showed Cloud Push working over WiFi, LTE, and 3G, so I will test again from other locations.
My previous test that showed labs working but not the public demo was a test error: labs and the public demo have different APNS certificates, so cannot work simultaneously.
Jack, please report on your testing under different network conditions.
A test of Cloud Push this morning did work. I will retest under different network conditions.