My Brother ADS-2000e doesn't work any more with Mac OS Catalina. Is there something I can do to fix it?

Brother lists that as a device that they support for Catalina -- see the lower section of https://support.brother.com/g/s/id/os/macintosh.html

You can download the driver from Brother at: https://support.brother.com/g/b/downloadtop.aspx?c=us&lang=en&prod=ads2000e_us

As I said, if nothing else works, then VueScan is your only Catalina option. Less expensive than a new scanner, and vendor software independence from now on. Your other option, if you performed a Time Machine backup of your previous version of macOS is to boot into Recovery, and perform a Restore from Time Machine Backup.

There is price, value, and opportunity cost. They are inequalities, so choose wisely.

I have owned VueScan Professional since 2010 and continue to use it with a long unsupported Canon scanner. Because I purchased the more expensive Professional version, I have never paid an annual upgrade fee. I receive no benefit from the VueScan vendor for recommending it here.

Reboot the Mac, and see if that changes the situation. If nothing that you try gets the scanner working again, then the paid, non-subscription, 64-bit VueScan product can drive this device without any Brother software or drivers installed.