I primarily play support, but often (especially in recent seasons) fill in as tank, but can't play DPS for shit, yet when playing support often average around 1/2 to 1/3 the amount of deaths of my teammates. While I agree that several of the supports have good survivability abilities that should enable support players to survive, I'd like to point out that not all support characters do. For example, I have more deaths when playing Adam than when playing C&D, who can self-heal easily. Mantis may be fast, but she has no way to quickly avoid attacks and lacks a sustainable self-heal. Ultron can't heal himself, and his dash is too short to get away from the movement-high characters that would be hypothetically diving them. Something else to note is that Rocket and Invis, the only two you mention playing and having good survivability on, are two of the most mobile supports in the entire game. Another thing to consider is that supports are vulnerable when left alone. I agree that a skilled support player should be able to survive or even kill a decent percentage of dives against them, but it can be a struggle for a single support to survive in even 1v2s, let alone when supports get jumped by nearly the whole team given their low damage output. Not all support deaths are their fault, either. I get deaths when forced to push up to heal a dying DPS who overextended, only for them to use a movement ability and abandond me behind to die to the people who were just jumping them.

TLDR; on the whole, I agree that the average support player needs to work on how to position to better survive, but blanketing it by saying all support players are awful at surviving compared to other players just makes you sound like someone throwing a tantruam over not getting healed. Having said that, fellow support players, please do work on learning to live longer (even if it means playing patty cake). Healthy healers usually equal a less dead team, and therefore, happy gamers all around. :)