Why didn’t The Avengers and S.H.I.E.L.D. agents show up to help Tony in what was very clearly a dire hour of need?
Spoilers for Captain America: The Winter Soldier, Iron Man 3, Thor, Agents of SHIELD below.
SHIELDs absence explanation:
In Captain America: The Winter Soldier we learn that Hydra secretly infiltrated SHIELD in the early days of it's formation, and have been shaping world events ever since, including the death of Howard Stark and the assassination of JFK. They specifically mention that they have been funding terrorist groups, and as such it is safe to say that the 10 Ring Terorrist group (which turns out to be AIM) were funded by Hydra, and as such their activites were being masked from SHIELD from with in. This is further backed up by Hydra having access to Extremis in Agents of SHIELD (although at first they are at known as Centipede in early episodes).
As for The Avengers:
Captain America, Black Widow and Hawkeye all work for SHIELD, and as such wouldn't have known this was occuring as it could have been hidden from them. Thor was off world fighting the rebellion caused by the Bifrost being destroyed in Thor. However, Bruce Banners location thoughout what is known as "Phase 2" of the Marvel films is still currently unknown.
- Thor lives in Asgard most of the time. Until they repair the technology/magic which creates the Rainbow bridge, I suspect commuting is out of the question.
- The Hulk: As seen in the Avenger's movie, it is likely the Hulk spends his time as far away from other people who know who he is as possible. An eight hour window probably makes getting his attention challenging. Nor is he known for his subtlety. The last thing you want is HULK SMASHING his way toward the problem you are trying to sneak up on.
- Hawkeye and Black Widow are both SHIELD operatives and could easily be on assignments anywhere on the planet. While they might be perfect for the job, they could just as easily be in Kazakhstan doing a secret operation.
- Captain America, currently a fellow out of time, is probably being brought up to speed and likely living in a SHIELD base while he catches up on the last sixty years of history. He would likely be very concerned if he knew of the kidnapping but no information had been made public at the time, so he would not be mobilized either.
Kevin Feige, Marvel Studios President stated in an interview:
Journalist: After cell phones came out horror directors had to come up with elaborate ways to explain why people wouldn’t call someone on a cell phone for help, now that all The Avengers know each other do you have to come up with excuses for why Tony Stark wouldn’t reach out when he needs a hand?
Feige: It’s a good question, and it’s sort of half and half. I am betting that like the comics you don’t have to keep – if you are reading a standalone “Iron Man” comic, they don’t spend every page explaining where every other Marvel hero is. The audience kind of accepts that there are times when they’re on their own and there are times when they are together. I’m betting that movie audiences will feel the same way. That being said, there is a little bit of lip service here and there to that. There is also just the very nature of Tony wants to, once he barely survives that house attack you saw today, and even you saw it in the message he left for Pepper, he’s basically saying “I’m going off the grid to try to figure something out.”