imac memory card reader

Bring up the Finder app and go into your Finder menu and choose Preferences.

On the General tab you can indicate if you want external disks displayed as an icon on your desktop.

In the Sidebar tab you can turn on "External disks" to show up in your Favorites list.

You can also use Disk Utility app to unmount/eject SD cards, but Finder is generally preferable. If it's being glitchy you may need to go into the Disk Utility to unmount it, then re-mount it.

Boot into Safe Mode according to Start up your Mac in safe mode - Apple Support and see if the problem persists. Reboot normally and check again.

NOTE: Safe Mode boot can take up to 10 minutes as it's doing the following; 

• Verifies your startup disk and attempts to repair directory issues, if needed

• Loads only required kernel extensions (prevents 3rd party kernel/extensions from loading)

• Prevents Startup Items and Login Items from opening automatically

• Disables user-installed fonts 

• Deletes font caches, kernel cache, and other system cache files

You would want to see if the SD CARD is detected well, mounts, and unmounts in the Disk U utility app. And you would want to try a different SD Card as well before concluding anything. Something the Mac can be a bit finicky in recognizing the SD Card, however if apply gentle upward pressure or gentle downward pressure gets the SD Card to be recognized then it is the reader itself.

Most likely though, assuming it's not hardware, you should try ejecting (i.e. un-mounting) in Disk Utility. Unlike trying to eject normally from Finder, unmounting from Disk Utility app will usually tell you which specific process/app is locking the card. Also, even Disk Utility it says it can't unmount it because ______ app has it locked, trying again in another 30 seconds will usually allow you to safely unmount it.