When running in analogue mode, batteries can last for days or even weeks if used infrequently. But when in digital mode, battery life suffers significantly. The decoder circuits (microprocessor, DAC, RAM, etc) are all power-hungry devices. DAB+ uses the AAC codec which is complex to decode, leading to increased signal processing requirements and the need for a powerful microprocessor. It means the receiver can only run for several dozen hours on battery power.
In analogue receivers, most of the electrical power is used to run the audio amplification stages. Very little is needed to run the receiving end of the radio. The opposite is true for DAB+ radios. Most of the electricity is used in the receiving and decoding stages, whist comparatively little is used for audio output. So running a DAB radio at low audio volume will not significantly enhance battery life as it does for an analogue radio.
If you are using a digital radio on batteries we suggest that you invest in some good quality rechargeable batteries that will save you money over the life of the product.