There is a bug that transforms all quest reward items when you start a new game. I don't know why, but that's what happens and it always happens, so you can't just get lucky and keep your stuff.
If you give any quest uniques to Gillian before you start a new game, it should retain it's stats, at least it worked for the magic rock unique for me. If she's not storing any items for you try running the "Run_Hell.exe" instead of TH.