I think the question to ask yourself is not whether your daughter has a chance of passing the 11+, but whether the best available school FOR HER happens to be a grammar. If you think that it is, give the 11+ a go. If not, don't. What are her primary school's concerns? Is it just that they don't think she will pass the exams, and is therefore being set up to fail, or do the feel that she would struggle in a grammar setting? What alternative schools do you have?
There are worse things (even educationally
) than not passing the 11+. one of them is to scrape into a school where you cannot keep up. I have seen the damage that can do; I had friends at my academic, private school who suffered years of stress and eroding self-confidence despite the fact that, nationally speaking, they were probably well above average ability.
Those I still hear of are now, I believe, successful women with satisfying jobs (generally in creative or caring arenas) and happy families of their own. They have survived and gradually rebuilt their self-confidence. But in some cases that took years. The "lucky" ones were probably those whose parents bit the bullet and moved them to less academic schools in the first couple of years of secondary education. I have two friends who moved and, with a more suitable teaching pace/ more support, went on to achieve much better grades than they would probably have done at our school. Instead of being bottom all the time one became head girl, the other has a post-grad degree etc. Of those that stayed, one actually ended up sitting her O-levels in a psychiatric hospital...
You might get the impression from that that my school was a callous exam-factory. It wasn't. The staff cared deeply about the pupils and went above and beyond their duties to try to get the best out of each of them. There was also no teasing or bullying about marks etc. with girls genuinely trying to support all their form mates. The pressure came from within these girls themselves (and in some cases their families). If you cannot do the work, no-one can hide that from you!