I would say please make it persist through Death. There would be nothing more frustrating / annoying than being in a game with some folks and the group wipes so everyone leaves because the lost their buff.
Also I like the idea of the stacking buff so that if you want the really rare items or want the extra challenge (or because you have more time ) you can go for a bunch of rare / champion mobs then on to the boss.
I also wonder if there is a possible tie in here whereby increasing the buff also increases a buff on the boss (to make it harder to kill)?
Which would be like an optional challenge mode.