Try cleaning the contacts. Get some spray contect cleaner, Spray it on a SD card contacts and insert it and remove it a few times. Try this 2 or 3 time with new spray on the card contacts.
DO NOT SPRAY IT INTO THE SD CARD SLOT.
If thast doesn't solve the problem the only other thing you can do is replace the motherboard as the SD card slot system is solder onto the motherboard.
That is if you have done everything else to try and fix it. Like a Clean install of the operating system.
Oh and make sure the cards aren't Locked.
If you are using a DSLR camera, like for example a Canon 60D, there may be an option to use a "Low-Level Formatting" on the card. This should make it writable when putting it into the computer.
To test this (and confirm it works) I did the following:
Canon 60D camera body
Sandisk 32GB SDHC Extreme Card
Macbook Pro 15" (mid 2010 model) with built-in SD card slot.
Place SDHC card into camera (SD card may work as well). Navigate through menu until you arrive at settings that allow the camera to format the card. There may be an option to format it "low-level", which you would then select.
-Note that all files on card will be erased permanently.-
After the camera formats, eject the card from the camera, and place inside the built-in SD slot on the Macbook.
The card should automatically mount, containing both read and write priviledges.
Hope that helps.
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