Why do our updates fail?
We have version 5.0.33 - yes, I know it's old, but every time we try to update we get a message that "update could not be installed (patch apply failed)"
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I've filed a report (after restarting successfully) with report ID 1975415356.
Start by uninstalling Zotero and making sure it's gone completely from C:\Program Files (x86)\Zotero Standalone and C:\Program Files (x86)\Zotero. Your data will be unaffected. Then try reinstalling Zotero 5.0.57 for Windows and see what happens if you try to upgrade to 5.0.58 via Help → Check for Updates. (For others reading this later, you can change the URL on the download page to specify a particular version. In general, if you're doing this, you'd want to try the version one behind the current one.)