It sounds like you've already taken some top-notch initial steps. If the device is still not recognized after updating the drivers and testing different SD cards, you might want to check if there's a BIOS update available for your laptop that can address hardware compatibility issues. Additionally, check in the Device Manager to see if the card reader is listed under "Storage controllers" or similar entries; if it has a yellow exclamation mark, right-click on it and select "Uninstall device," then restart your computer to let Windows attempt to reinstall the driver automatically.
If those steps don't work, consider manually downloading and installing an older version of the JMicron driver—sometimes newer versions can introduce new issues. Lastly, ensure that any physical connections are secure and that there isn’t dust or debris in the card slot which could be causing a poor connection.