I thought about Nelo Angelo yesterday and I have a little theory.
What if Nelo Angelo (Vergil)'s armor exists to suppress his power?
When Vergil fought Mundus (in the end of DMC 3) and failed, Mundus knew that Vergil was the son of Sparda, so instead of killing him, he enslaved Vergil. Then he saw that Vergil's powers were little (he was not aware of previous Vergil vs. Dante fight), so Mundus decided to share his power with Vergil (Nelo Angelo now). Suddenly, Nelo recovered from the fights and his power grew in several times. He was strong enough to defeat Mundus, so Mundus decided to suppress his force potential with this armor.
Knowing this, I can say what happened to Nelo after the third fight with Dante. You maybe noticed that when Vergil removed his helmet he became much powerful than he was in previous confrontations. When Dante defeated him, Nelo (by this time, 100 % Vergil) decided to unleash his full power. Then, a "defense mechanism" worked. "Defense mechanism" is another part of my theory. Mundus was not intended to lose such a powerful servant, so he designed a "defense mechanism", which included three levels of defensive measures:
Level one: If Nelo (Vergil) remember who is he with his armor on.
Level two: If Vergil realises how to take power from his reserves.
Level three: If Vergil remember everything in level 2 condition and/or he decides to enable all his reserves of power.
Vergil reached level 3 condition after 3rd fight with Dante. He holded his head, which is probably the sign of mechanism working. When he began to activate his powers, Mundus just annihilated him.
If you've got any questions, just ask me