Taxonomies disappear after upgrade: WP 4.4.7 -> 4.7.2

A client's wordpress site uses Custompress. I haven't done any updates since 2015, and am now upgrading the system from the version stated in title. I have updated CP from 1.3.5.3 to 1.3.59 and everything works fine.

I have spent the last day trying to resolve why one of my custompress custom content type taxonomies are disappearing.

I have updated all plugins and the taxonomies remain, but when I upgrade WP from 4.4.7 to 4.7.2 they disappear.

Wordpress then wants to do a database update. After this, the taxonomies are gone.

What's really weird is that I can step back the file system to 4.4.7 and then WP wants to do a database upgrade, and the taxonomies appear again?

So they're obviously not been overwritten during the upgrade process from 4.4.7 to 4.7.2

Any help would be greatly appreciated!