|You didn't mention whether your external drive has a 3.5" hard drive inside of it and came with an external power adapter, or it has a 2.5" hard drive inside of it (often called a "portable"external hard drive) which does not come with a power adapter.|
The USB port supplies only +5 v DC.
The USB port (or two USB ports) MUST be able to supply 500 ma of current for an external hard drive, or an external optical drive.
3.5" (desktop sized) drives require both +12 v and +5 v DC.
The hard drive can't get enough current at +5 v from just the USB connection(s) to the computer.
2.5" (laptop sized) drives require only +5 v DC.
Usually the hard drive CAN get enough current at +5 v from just the USB connection(s) to the computer, if it (they) can supply 500 ma, unless it's an older larger capacity 2.5" drive inside the external enclosure.
If it DOES have a 3.5" drive (or more than one of them) inside of it and it DID come with a power adapter, you MUST use that power adapter because it supplies +12 v and some additional power (current) at +5 v to the external enclosure and the hard drive, and that power adapter must work properly and have nothing wrong with it's connection to the external enclosure.
I have never seen an external (3.5") drive that has a built in power adapter - they have all had an external power adapter.
You must be talking about a problem with the cord for that external power adapter or it's connection.
It's common for people to pull on the cord rather than the plug on the end of the cord when they unplug an AC to DC power adapter. Eventually the plug on the end of the cord, or the wires inside the cord near the plug, are likely to get damaged when that is done too often. That's a frequent problem with AC adapters for laptops, but that can happen with any external AC to DC power adapter's cord.
If the wires inside the cord near the plug get damaged such that they short to each other, the power adapter can be burnt out easily.
You can buy the same type of plug (same hole diameter, same outer diameter - if the hole is too big you'll have problems). and connect, preferably solder, the wires inside the cable to it, if the adapter hasn't been damaged, but if you continue to pull on the cord rather than the plug on the end of the cord when you unplug the power adapter, that won't last as long as a plug that's molded into the end of the cord.