A lot of car chargers charge at the same rate as USB from your computer, which is half that of a wall charger. For most phones this is not enough to keep up with any sort of use. I would suggest looking into purchasing a high speed car charger. I know Verizon sells one (that's the one I have), but you can get one just about anywhere that sells cellphone accessories (except maybe the has station), just make sure it's for micro USB and says high speed charger.
I love that you're using your phone as your music player bessex23. But demmo86rt is right, the car charger really isn't meant for a replacement to a wall charger, more of a boost between charges. Car chargers and a charge through the USB of a computer provide a lower amount of charge than a wall charger. So an application like the media player that uses more battery than, say, email running in the background, may drain the battery faster than the car charger can charge it. To make sure your phone is getting the best charge possible, make sure your Droid 4 charger is meant for your Droid 4 and preferably by Motorola. Some Micro USB chargers are meant for Bluetooth headsets and don't provide the same power supply. You can take a look at all the accessories available through Verizon Wireless at http://bit.ly/p5r0fh.
There's also some additional suggestions on improving your battery life at http://bit.ly/I1kuOG.
Let me know if there's anything else I can assist with.
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