I am happy to declare that uninstalling then repairing permissions and then reinstalling Sophos for a second time actually fixed the errors. When the updates arrive, the product momentarily turns off on-access scanning (the shield turns grey) but it turns back on in a second or two. This still shouldn't happen, but I assume this issue, along with the other issues (disappearing icons, fatal errors, etc.) will be fixed in the 8.0.7 update.
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