You have my sympathies and support. Life is no doubt difficult enough without this to deal with too. It sounds to me like your child is effectively being penalised for having a medical condition. These sorts of incentives that children cannot reach - through no fault of their own - really bother me (I am a school counsellor in training). Yes good attendance is important, and families should be supported where possible to have their child in school. But this is not a situation where there is a lack of desire to attend.
Those who say 'life isn't fair, teach your child that' seem to me to be completely lacking in empathy and understanding here. This child has a medical condition and she and her family are probably well aware of how unfair life can be on a daily basis. One size does not fit all and the "Every Child matters" government policy is centred on allowing each child to be able to work towards goals in an individualized manner.
One way to seek further advice may be through - https://www.citizensadvice.org.uk/famil ... n-schools/
I see you say you can't take it further with the school but I just wonder if the SENCO/school counsellor or some sympathetic member of staff might advocate on your behalf here? With some persuasion, could the school arrange for some other reward for your child working to the best of her ability - within the constraints of her illness? If they absolutely will not budge and you are otherwise happy with the school, could you arrange a reward for your child yourself (although this may seem galling to have to consider?) I wish you the best of luck and it is clear how hard you are working to support your child here.