You can't just equip an EVA suit, you have to turn it on. The button that appears on the top left of your power bar. The suit's headlight will turn on to tell you that it is 'active'- no light, no protection.
Yeah I had simular issues, even when I had activated mine it didnt seem to stop my toon slowly dying. I did find turning the suit off and on helped... oh and dying atleast once!
Best way though would be to turn it on before your character starts dying, so have it on before you enter,