i have noticed everyone that has the "Carry more ammo for Heavy Weapons." buff from raid gear loses heavy ammo when they die. I have heard others say say it will go to 0 ammo but I personally only go down to 1 (I am speaking on rocket shells).
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I can confirm that the Carry heavy weapon perk does indeed cause you to lose heavy ammo on respawn. My buddy has a exotic chest that has this perk and when ever he would die he would lose hevery ammo. I ask him to put on another chest piece that did not have the perk and his ammo stop disappearing.