Once Nullhide Ferox's activated ability has resolved, it can gain new abilities. It won't lose those abilities.

Nullhide Ferox's activated ability can be activated only while it's on the battlefield. Players can't, for example, activate it to try to stop its replacement effect from putting it onto the battlefield.

Once Nullhide Ferox has lost its activated ability that makes it lose its abilities, that ability can't be activated again until the turn's over.