I had the same problem for weeks, and the steps below worked for me:
1) Completely uninstall the Salesforce Extension Pack VS Code extension
(to uninstall all sub-components of the package).
2) Uninstall Salesforce CLI:
MacOS / Linux
Run these commands from Terminal
sudo rm -rf /usr/local/sfdx sudo rm -rf /usr/local/lib/sfdx sudo rm -rf /usr/local/bin/sfdx sudo rm -rf ~/.local/share/sfdx ~/.config/sfdx ~/.cache/sfdx sudo rm -rf ~/Library/Caches/sfdx sudo rm -rf /usr/local/sf sudo rm -rf /usr/local/bin/sf
Windows
Select Start > Control Panel > Programs > Programs and Features.
Select SFDX CLI, and click Uninstall.
Inside your home directory, delete these two directories:
.config\sfdx .config\sf
If the CLI is still installed, delete the %LOCALAPPDATA%\sfdx directory in Program Files.
More info- https://developer.salesforce.com/docs/atlas.en-us.sfdx_setup.meta/sfdx_setup/sfdx_setup_uninstall.htm
3) Re-install Salesforce CLI
Follow the steps on this page depending on your OS. I use MacOS, and the steps for installing the .pkg file worked easiest for me.
4) Re-install the Salesforce Extension Pack VS Code extension
I installed the "Expanded" version version this time, and had previously used the original version, but this shouldn't matter.
5) Re-start VS Code
That should do the trick. I immediately was able to deploy/retrieve to various sandboxes without even having to Re-authorize the orgs, when before completing these steps I was experiencing the SFDX bug.
SFDX: Authorize an Orgcommand again, complete the authentication, and then re-start VS Code it starts working again. But then by the next day same problem re-appears. The only thing I haven't tried yet is uninstalling/re-installing VS Code and all extensions. I have a feeling it's something broken within the Salesforce Extension Pack extension with how my Org Alias settings are saved to my User. Running Deploy/Retrieve commands from the Terminal always works, however, so the CLI appears to not be the issue