Why all this talk of "failure"? That's a very unhelpful and negative word that isn't actually used by the selective schools, so I don't know where it comes from.
At the end of the day, the grammar school will take the top "x" number of pupils - if they have 100 places, they'll take the "top" 100 on their list of applicants (ordered by whatever criteria they choose to use such as the 11+ results, distance from school, catchment area, etc.). That doesn't mean everyone else has "failed", it means that they weren't in the top 100 on their list. Grammar schools don't write a letter saying your child has failed the 11+, they send a letter saying that your child wasn't successful in obtaining a place.
Exactly the same as faith schools. You don't get a rejection letter saying you're not faithful enough, you get a letter saying other children satisfied the criteria better than you (i.e. more points and/or nearer).
In any form of selection, some applicants get in and others don't. At the end of the day, it depends on the applicants that year. In lower birth years, children will be offered a place who live further away or who got a lower score in their 11+ tests than in other years where the birth rates were higher. It's just competition. Like everything else in life.
When we were going through it with our son, we embargoed any mention of the words "pass" or "fail". We made it quite clear, from the moment that secondary schools were mentioned, that schools had a specific number of places available and that if more children than that applied, they'd have to use some form of selection procedure. We discussed the faith school criteria at length with him so he knew that it depended on church points and distance from school. We discussed the grammar school at length with him, so he understood that distance from school and results of the 11+ test both influenced their choice of who to offer a place to. He understood that it wasn't just dependent upon how well he did in the 11+ exam, but more importantly how well everyone else did, and that even if he did a brilliant test day and scored 75%, 85% or 95%, he could still not be offered a place if there were enough children who scored more and/or who lived closer. And more importantly, that if it was a hard paper and he struggled, then others would have struggled too and he may still be in with a fighting chance if he did better than others.
We were all very relaxed about the whole thing - we prepared him well and we know he tried his best. The actual 11+ day was a real anti-climax and was the day of opening the grammar school letter. If it had been a "sorry you havn't been offered a place", he certainly wouldn't have felt a "failure". It's all about managing expectations and properly discussing things with your child.