"Nie widzimy naszych mężczyzn."

Translation: We do not see our men.

[danfeve]

Any idea which case is this? I can't find any for which the plural for nouns needs to remove the last vowel and ends with N.

[mihxal]

Plural genitive. You can read more about it for example here:
https://www.duolingo.com/comment/13516854

[Raicuparta]

I tried "We are not seeing our man" and it failed. Does it not mean the same thing?

[mihxal]

Generally, English usually doesn't use Present Continous with verbs of sensation: http://english.stackexchange.com/questions/5904/in-what-case-you-would-say-i-am-seeing-instead-of-i-see