Regarding the function of the sdcard/s in question: If a card is reading and writing without issue inside your camera, that’s a good sign that card is functioning properly. However, you can try the following:
- After backing up the data on the sdcard, format it with your camera.
- Insert the card into your reader and check if your PC 'sees the card.’
- If the card does not show up, try having a friend (with a working reader) format the card on their computer and try again.
Skip to the end of this answer for an explanation of this process.
As far as USB card readers go, they can malfunction for a variety of reasons that may or may-not be related to the reader itself.
Here are a few steps for troubleshooting the reader:
- If the card reader is connected to a USB hub, try connecting it directly to your computer.
- If the reader is already directly-connected, try using a different port*.
- If the reader has a detachable USB cable, try swapping it out for another.
- Lastly, try using the reader on another computer.
If all these steps fail, it may be time to pickup a new card reader.
(*USB ports often come in pairs, if possible, connect to another port as far away from the one you’ve been using as possible.)
Formatting the card (which is different from deleting all images or 'clearing' it) is a process that prepares the card to store files, by establishing a file system. Removable media, like sdcards or USB flash/thumb drives, occasionally end up with errors in the file system on the card. The most common cause of such errors, is a card being 'removed' (unmounted) incorrectly e.g., a card is taken out of the reader, while the computer is still accessing it.
It is possible for your sdcard to function inside the camera, but to be unreadable on your PC, when such file system errors occur. (Re)Formatting the card will effectively erase all data on the card and will re-create the necessary file system.