If FM's fine and DAB isn't, it sounds rather like a signal issue. Are you near any of the grey areas on this map?
http://www.ukdigitalradio.com/images/coverage-map.jpg
There are very few areas of the UK where FM is unavailable (mostly Snowdonia and Scottish Highlands), but DAB can be much more patchy - even here in the Chilterns (green on the map) it drops in and out occasionally (I guess as it switches between Oxford and London transmitters).