They always have died like men and that's actually the point. Once again it comes down to context:when did the people of Israel not "die like men?
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Psa 82:6 I said, "You are gods, sons of the Most High, all of you;
Psa 82:7 nevertheless, like men you shall die, and fall like any prince." (ESV)
Notice what God says in verse 6--'"You are gods."' He calls them gods because they are his representatives, his judges. But they have been abusing their authority and were "[judging] unjustly and show[ing] partiality to the wicked" (vs 2). In verse 7, God is simply reminding them that despite his having called them "gods, sons of the Most High," they are still men and not immortal.