You can create categories using dynamic categories rules to simplify the process of assigning products to categories. Magento 2 Dynamic Categories extension is just the module you need since it allows you to:
- generate products to categories based on product attributes
- remove all products from the category you want to generate products to
- remove products you want to add t a certain category from all other categories it is contained in
- add products to a category based on catalog price rules
- preview products that are going to be generated according to conditions you set
This module may solve your issues with the products disappearing. And the cron job it runs by will automatically update and assign new products to categories if they fall under the rule conditions.