This sounds like an impedance mismatch. If the aux input on the car's head unit is expecting a line level input, that is typically over 200Ω and can reach to several 1000Ω, whereas typical headphone output -- I'm not familiar with your device but am thinking you are using the headphone output -- can be 100Ω or less. The voltage output may be insufficient also; I know that some Apple devices are around 2V whereas some domestic audio devices reach twice that on their outputs, for example.
If you can use a proper line out from your source device, try that and not headphone output.
ED: Since players do this because they are relying on batteries, I wonder if powering the player would improve your situation. I doubt it, but it'd be clever if the maker made this provision.