Haven't read through the thread but ex nursery manager here.
Your poor child. That really is a lot of illness and sounds awful.
I would be concerned about infection control, cleaning and implementation of Health and Safety Policies.
Yes, children get unwell when they start Nursery as they build up their immunity, but that sounds extreme. Also the time of year means bugs are rife.
All the more reason for Nurseries to be strict.
I would be questioning things like hand washing procedures for the children, as well as appropriate ventilation. As well as cleaning and frequency of toys/ bathrooms etc
I would be concerned about the Managements role in ensuring unwell children stay off. For example, a child who is sick, should always stay off for 48 hours. Regardless.
As a Manager I used to hear it all. Something they ate etc etc
As nurseries are predominately used by working parents , many don't even tell you that their child is unwell in the first place.
You discover it a few hours down the line, when the Calpol wears off or they are sick.
It's absolutely poor parenting but I'm not on here to criticise that.
Definitely speak to the Manager and go with your gut.
There are poor Nurseries and there are good Nurseries and it doesn't sound as though the one your child attends is particularly good.