Both USB drives are failing to read my USB flash drives. I can still print fine to a printer using a USB cable. I have had difficulty for a while backing up to an external hard drive that uses a USB for a power source. What is causing this problem?
This sounds like a power issue given the only USB devices that are failing to operate are all devices that require the USB port to power the device for operation in the first place.
The first question to ask is whether this happens only on battery, only on power brick, or on both? If you can isolate the problem down to a specific power source, then it's possible the power source in question is on the verge of failing and is contributing to the problem at hand. Once you do that, the fix becomes as simple as replacing the part, either the battery or the power supply.
If it happens with both power sources independently and used together at the same time, there may be a more serious issue with the laptop's motherboard itself. One point of concern that I have is if the system is incapable of fully providing power to the USB port, it may be underpowering other devices as well, such as the hard drive, which can potentially lead to data corruption and loss. If it falls into this category, it's going to be a lot more difficult to track down and fix... however, as a short term gap until it starts to break hard, you could always utilize a powered USB hub for devices requiring power to operate (such as thumb drives and external hard drives that pull power from the USB bus).
That should get you started with the obvious stuff. Best of luck!