How is it possible to take 7 days to rescue the trapped survivors in the train crash? I'm asking about episode 9, in which Otonashi remembered that in his past life, he was involved in a train crash accident. The illogical thing is: what on earth takes the rescue team so long to notice there are people trapped in there and to actually rescue them? It took them 7 days! That is, a full week!
It might appear absurd to some people (maybe it really is), but I think there is an in-universe (in-Keyverse) reason: they were forgotten. I have thought about it when answering this question that since Jun Maeda doesn't have many tricks up his sleeves, it must be explainable with the logic from his other works. And I think I've found it in One (and in Little Busters!):


  Someone about to leave to the Eternal World starts to be forgotten approximately one week before going.


Note that the mechanisms in the Eternal World are really the same as those in the Afterlife World. In One, Kouhei was banished to the Eternal World because he broke the pledge with his deceased younger sister, that he would always remember her, by going out with other girls and therefore forgetting about his younger sister. That is exactly what happened to Otonashi: his purpose in life used to be his younger sister, Hatsune, but she died of illness. After observing a fully recovered child ready to leave the hospital, he made up his mind that he would live for someone else, to save that someone from dying from illnesses. Thus, he broke the pledge with Hatsune, as his center of life was no longer his younger sister, so he would receive his punishment by being sent to the Afterlife World.


  However, he or she is remembered the moment that person returns. If a strong emotional bond is established in the real world before leaving, a person in the Eternal World can be returned after approximately one year.


He established a strong emotional bond with Kanade when he signed the organs donor card (it could be that she received her heart from Otonashi or someone else, but she didn't know whom for sure), so it ensured his return to the real world after approximately one year (so he didn't pass on with the rest because it hadn't been one year since his arrival in the Afterlife World, but this may need a separate question and answer to explain).

I surmise that his experience in the Afterlife World could be training Otonashi to cope with loss and thinking for himself for once (like being able to love a girl). Then when he comes back stronger (waking up in the real world again), then it could follow the story of Little Busters!:


   Rejecting this turn of events, Rin travels back into the artificial world again (this time created by Riki and Rin) and helps Riki overcome his weakness. Afterwards, the two of them go back to waking up at the crash site. This time, Riki and Rin work together to save everyone at the crash scene. Kyousuke, who sneaked onto the bus (as a third year he was not allowed to go), managed to block the leak hole on the gas tank to delay the explosion, despite his injuries being far greater than anyone else. Everyone in the bus recovers from their injuries, although Kyousuke's recovery takes longer due to extensive injuries. Finally, after Kyousuke returns, he rents a minibus, and the members of the Little Busters set out for a trip to the ocean.


So somehow his abdominal injuries didn't take his life and he met Kanade again.