Iirc, you will not keep items when you get defeated. For story battles you'll need to load a previous state, so logically no. But even if it's an optional battle where you can continue playing you won't keep items. And if you use the "restart battle" option you need to collect everything again. The only thing you keep is experience gained. The stuff you will keep only after a successful battle is the stuff listed after a successful battle: items, gold, skill points.
There are lots of rare or even unique items to be found via digging, especially in the second half of the game, and in the Obel Ruins. There are some more ways to get nice stuff: quests rewards and stealing (Noah). Getting S ranks after battles will give you a unique item, but only one per stage (you'll never get more than one, even in NG+). The most difficult is to get the dig items AND S rank, because taking too much time with Rene will result in a lower rank. Luckily you can find a lot of very helpful tipps here in this board. And KFCrispy has even started a video guide: https://www.youtube.com/watch?v=tXk0WrX ... eBQUfNV30Q