When you are unable to find the connected SD card either on your Desktop or in the Finder's sidebar, you need to check whether the SD card appears in Disk Utility, Mac's drive manager. If it shows up there, it means Mac successfully detects the SD card, otherwise, Mac fails to recognize the SD card.
Go to Disk Utility to check if Mac detects the SD card: Launch Disk Utility from the Launchpad, click the View button and select Show All Devices, then check whether the SD card is listed in the left sidebar.
If the SD card shows up in Disk Utility, you can try to change the preferences of Finder to make the SD card show up on Mac. Just go ahead to Finder, click Finder on the top menu bar and choose Preferences. From the General tab, check the box of External disks under Show these items on the desktop; from the Sidebar tab, check the box of External disks under locations to show it in Finder's sidebar.
Perhaps the SD card is greyed out in the Disk Utility and the SD card is not mounted on Mac, you can try the methods below to fix it. Given that the SD card not showing up on Mac poses a risk of data loss, you can recover data from the SD card as many as possible before proceeding to fix it. Try iBoysoft Data Recovery, the professional data recovery software.
Method 1. Manually mount the SD card in Disk Utility
Method 2. Repair SD card with First Aid.
Method 3. Update disk driver on Mac.
Method 4. Reformat the SD card to get rid of the incompatible file system or corruption issues (this erases all data).
If the SD card disappears from the Disk Utility, it means Mac can't recognize it, you can apply these methods to troubleshoot:
Method 1. Check the connection and restart your Mac.
Method 2. Check if the SD card is locked or damaged.
Method 3. Check if the SD card reader is not working.