I've been using Sourcetree for years without this issue. Recently, my antivirus software has been preventing Sourcetree from opening. Last time this happened (last week), updating my AV software solved the problem. Now, no updates are available for it, and I cannot open Sourcetree. No logs are created by the app, so it seems that it doesn't actually attempt to launch. Perhaps it's an issue with the Updater?

I went to check the app's digital signature before making an exception for the app in my AV software, and the signature did not have a timestamp and is using SHA1. Could this be the issue?