When should I let my teammates die?

Never let someone die intentionally. TTK in Overwatch is low -- Heroes will be dying around you regardless, despite your best efforts.

On the other hand, as long as you're constantly healing your allies, you're generating a lot of Ultimate -- so a better question is not, "When should I let my teammates die", but "When should-- HEROES NEVER DIE!".

Personally, If you can land a rez for 2+ heroes, do it -- sitting on your Ultimate won't do anything, and saving it the entire match is the same as not using it. Whether you're on Attack or Defense, you should save it for a concerted push, where the sudden additional allies can swing the battle back in your favor (or secure an already overwhelming advantage as the other team tries to run back).

The answer is: when you are going to die from healing them while your ultimate is ready.

Considering that Mercy is the No. 1 target of the enemies' concentrated fire, you'll have to accept that you should be really, really passive when your ultimate is ready. Your ultimate is useless when you're killed off first, after all. There is even an in-game tip making this clear.

Instead, convey them that your ultimate is ready, and ask them kindly to make a bold push through the enemy defense (or a relentless defense against the enemy force, if you're defending). When there is a severe loss on the team, peek into the spot and use your ultimate. This will allow your team to be relentless while making a significant progress, unlike when going relentlessly without your ultimate.

Your ultimate is sort of the panic button, so you shouldn't be letting people die for the sole purpose of rezzing them. However, there are occasions to let an ally die. The first rule on this is that no support can save a player who is determined to get themselves killed - if the player sees that you're healing them, and charges into the rest of the enemy team, the correct choice is to let them die and focus on protecting or buffing someone else; the alternative is that you both die. Boosting things like Reaper's Ultimate can pay off, but this is rare and the best choice for achieving it entails using Guardian Angel to fly in while the ability is active or immediately before its use (do not attempt this without coordination).

The second case, which is related to the first, where you should let a player die is if trying to help them would get you killed. The support player is often the most important player on the team, and you should prioritize your survival. This is particularly true for flankers, who will take you to dangerous places if doing their job right but who also have the tools to get out alive.

The third case is triage - it is acceptable to let one player die to keep a more valuable member of the team alive; losing Tracer to keep Reinhardt is a fair trade, for example.

The fourth case is priorities - it may be more valuable to buff, say, Pharah's Ult than to heal someone else. This is massively context dependent, and requires tactical awareness outside your own role.