They'd have all had scurvy, surely? Or is that what 'being delicate' meant? 
Every time there's a reference to the Robin or some other girl's 'delicacy', I remember that bit in Antonia Forest's Autumn Term where the newly-arrived Marlow twins get put in Third Remove ('with the stupids'), and everyone gets involved in making a sarky list in which you can opt to be either 'Backward', 'Delicate' or 'Plain Stupid', depending on your reason for being put in the form.
Note that the twins, who are genuinely 'delicate' and haven't been to school at all before now because of illness, opt for 'Plain Stupid', and the only one who insists seriously on being a 'Delicate' is laughed at. (Whereas EBD clearly thinks that being 'delicate' is more interesting, and even though she tells us several times early on in the series that the sparkling Tyrolean air has cured Joey's delicacy, it still doesn't stop her having lots of brushes with death...)
Also, Kingscote, which is very much not a school that specialises in delicate girls, seems to have some structures in place to suit the 'delicate' that the health-minded CS doesn't -- Third Remove, a class expected to have 'delicate' girls in it, isn't allowed to play netball because it's considered too exerting, only rounders, and there's a 'light' supper option for anyone off-colour or without appetite.