Just one more observation:
As i unfortunately have been one of the first ones that observed the problem with android 4.4.3 and then downgraded to the 4.4.2 radio to make rsap work again I for a long time skipped the upgrade to 4.4.4.
With Android 4.4.3 and the 4.4.2 radio I obeserved, especially with LTE enabled, often an excessive power drain while the radio was turned off (!). This was also visible in the battery information in the settings menue by the high percentage of the 'phone idle' consumption.
About a week ago I had some time to install 4.4.4., again with the 4.4.2 radio and the effect of high power consumption was gone again.
So if you have still 4.4.3 and also some strange energy loss problems, try 4.4.4.