Have you looked into getting a different adapter? If what plugs into your cigarette lighter for 12VDC spits out 5V at 2.4A, you're only looking at 12W of charging ability. Modern phones can easily eat more than than operationally.
A quick Amazon search pulls up this for $12. It can charge via USB-PD (type C) at 36W or QC 3.0 at 18W — but your phone model may or may not be compatible. Some research will be required on your part.
Since the phone is maintaining charge as opposed to draining completely, the wiring to the socket sounds like it's fine; it's the adapter that's your point of "failure" from the details provided.