It's a way of emphasizing 'all the time', or making known how important 'all the time' is to the speaker. Often it's said in a dry/ironic/sarcastic manner.
Usually we associate 'only' in some limiting manner - 'only once or twice' ie just a few times. So by adding 'all the time', as in 'only all the time', the fact that we are trying to put a limit on 'all the time' actually has the opposite effect and signifies that 'all the time' is very important to the speaker.
A similar expression is 'only forever'