You shouldn't lose it upon Fast Travel, only Death. It shouldn't serve as a debuff either.
The challenge should be "doing Patrol stuff without dying", not "doing Patrol stuff without dying or fast travelling and with bullet sponge enemies and basically no regen."
If it remains the way it is, at least make it so you can turn the damn thing off. We shouldn't have to lug it around and have it impede our progress everywhere we go if we don't want it to.
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I saw a post earlier tying it to faction rally emblems - equipped emblem on etc! (Can’t remember the originator for this idea)