How do I download my registered copy of Adobe Acrobat X Pro again?

If you upgraded to Catalina, this is nothing to do with deactivating. Catalina needs ALL NEW APPS. Apple designed it to make us need a big budget if we upgrade.

Um.... I'm afraid that's not possible because Acrobat X is no longer available.

Depending on what you need, you can get free Acrobat Reader DC or paid versions of Acrobat Standard or Acrobat Pro DC for US $12.99/month or $14.99/month respectively.  A 1 year subscription is required.

https://acrobat.adobe.com/us/en/acrobat/pdf-reader.html

https://acrobat.adobe.com/us/en/acrobat/acrobat-standard.html