A Mankey stole my looplet. Can I get it back?

I did a mission where I had to fight three Mankey. They had the move Covet, which stole one of my items and then teleported them to somewhere else in the floor. All three of them had stolen something, so I was chasing them down. I fainted one and got one item back, but after fainting the second, apparently it was the "leader" and the fight ended. That Mankey and the surviving one then escaped from the dungeon.

Unfortunately one of them was still carrying one of my looplets. Can I get it back?

There's no long worded answer for this. Simply no you can't. They're were boss NPCs with a unique id. You'll never find the same ones and every time you re enter the dungeon the game generates new NPCs with unique items(if they have any).

Items in Pokemon Mystery Dungeon aren't really rare, it shouldn't take long trying to get the same item back.

Unique items, such as the special treasures you can find, can be replaced by Cofagrigus for 50 gold bars if you lose them.