I tried applying for this for myself last year and got turned down because I have 'nothing wrong with me.' I mentionwd that I have problems with cooking (I'm over 16, so the forms are different for me than what they'd be for young children) and they decided that there should be no reason why I shouldn't be able to cook a meal for myself - yet I have less than 50% of my vision.
The CAB seem to think that they haven't even bothered to contact my GP or consultant at the eye infirmary. They were also surprised that I hadn't been for a medical before the DWP made their decision.
As I understand it, if your child has nystagmus they will almost certainly be classed as "visually impaired", i.e. their vision will never be fully corrected by wearing glasses or contact lenses. That in itself is considered a disability.
Unfortunately this does not automatically entitle someone to DLA. There appears to be alot of favouritism with the DWP giving people with certain conditions DLA and people with other (sometimes more serious) conditions nothing.
It appears to make no difference that I have been recently registered as partially sighted either.
It also does not appear to be related to equipment either - ideally there's alot of euipment I need (magnifying stuff mainly) and have been turned down. Yet my brother who is autistic has been awarded it.