There are two things to look at. first, I have had to replace my power cord at least once already because the cord got broken at the connector. The cord leaves the dock facing the front of the car, but the cord has to make a 180 degree turn the drop down the dash to my power outlet. Depending on how tight that turn is, you can damage your cord over time.
Secondly, you need to replace the OEM lighter plug with a higher power third party plug. The OEM does not output enough power to run the phone with the screen on, GPS on, etc. There have been many threads on this. But if you phone uses the battery and has less charge when you use the car dock after a trip than what you started the trip with, then this is the problem.