remove all usb devices from your computer with the exception of the mouse and keyboard then see this document
How to Reset NVRAM on your Mac - Apple Support
after resetting the NVRAM boot normally and attach the USB device directly to the computer, not a hub or keyboard.
If this does not resolve the issue you will need to either resore your computer to the instance where the OS and the reader worked using a time machine backup if you have one, or you will need to determine the brand and model and find a suitable driver from the manufacturer if one exists. Alternately you can see if another card reader maker has a 10.11 compatible reader.
Apple is most certainly not going to intentionally try and fix this regardless of where the fault lies.