Translate navigation menu in partner community

There is a known issue stating that the translation should be updated in the community 24 hours after you've updated the translation and published your community.

You could try adding another language to your community to see if this solves your problem. I recently had the same issue and contacted Salesforce support to get some help (to confirm if it's the known issue or another problem).

The support rep basically added another language to the community and doing that the translations suddenly appeared.

It's either that or they performed some internal magic that they don't want to tell us about :)