I will always try to go to you and assess my chances of revivng you and us both surviving it. I really can't see the point of me going down when you will be disorientated getting up, but if saving you means using a cobra because my current character can't bring enough DPS and I think we can spare it then, that's what they are for, no? Make it safe, then revive.
(...unless it's a hack or escort and you imagine you are "providing a distraction" on the other side of the map and are ignorant of the enemies around the objective. But the mission takes pririty, no? :innocent:)
I think in most cases (hacks and 'right next to you' excepted) we should just medigel on objective waves anyway... (this operation weekend excepted ofc)
When playing with my team I tend to find I often get there quickly (I like fast characters) start staggering enemies and another of the team revives. When that happens with PUGs I think the team often starts working better together. If you give up after 2 revives like OP says, then they won't be staying in your lobby long and you lose the chance to build on your teamwork and maybe make some friends.
Have fun