Update Dec 18th 2018 – Firmware version 2.10 has now been released for both the a7III and a7R III that fixes these issues.

Sony has suspended downloads of the latest firmware for both the a7 III and a7R III. They have also issued the following warning for anyone who has already updated the firmware to v2.00.

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It has come to our attention that the following issues may occur with our α7R III and α7 III interchangeable lens digital cameras.

1. In rare cases, your α7R III or α7 III model may stop functioning while writing RAW data onto an SD card that has already been used multiple times.

Notes:
This may also cause abnormalities in the files managing the images, preventing the images from displaying on the camera.
No image data in the memory card will be corrupted or deleted aside from data that was being written at the time the interruption occurred.
If images no longer display on the camera, follow the steps below to use the “Recover Image DB” feature:
Select MENU → (Setup) → [Recover Image DB] → desired memory card slot → [Enter].
Then, take a picture, back up your data on a PC or other device, and format the memory card on your camera.

2. With the α7R III, taking a picture while using the Auto Review function may occasionally cause the camera to stop responding.

We will provide updated system software addressing the above issues in mid-December. Until then, please take the following precautions.
Note: while we are preparing to provide new system software, we will no longer offer the current system software as an update.

Before taking new pictures, back-up your data and format the memory cards in both slots on the camera, or use a new memory card.
Ensure the Auto Review function is off when taking pictures.
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I updated my own a7 III and a7R III to firmware v2.00 but thankfully have not yet experienced these issues myself as yet.

You can also read this notification on Sony’s website here.