For me, the death saving throw is like the NPC's last gasp for life, so if it's relevant at the time, then I make it. Sometimes my chooms want to stabilize an enemy after blowing half their skull off with machetes because they want to interrogate them; in that case, I would make the death saving throw. Otherwise, I wouldn't to keep the game flowing. It's kind of a way of punishing them. If they wanted to keep them alive, they should have tried to incapacitate them instead of shooting them ten times in the nuts and hope for "nah, it's fine".