54 schools have identified cases since reopening.
Public health officials are asking schools to provide an out-of-hours contact number in case a member of staff or a student tests positive.
President of the National Association of Principals and Deputy Principals Alan Mongey says he wants an out of hours number for the Department of Health in return.
"I have no problem giving my mobile number if I can also ring someone else in the evening in the department to look for support, guidance and direction in terms of what has to be done.
"There is a kind of a continual expectation that principals and deputy principals are on call 24/7."
He said that principals are really at the end of their tether at the moment, even just with the hours they put in to get schools reopened.
The news comes as yesterday a survey from trade union Fórsa showed that only 49 per cent of schools provide Personal Protective Equipment (PPE) for special needs assistants (SNAs)
It also found that 17 per cent of SNAs also said that they had been asked to re-use PPE equipment.
Fórsa trade union represents more than 11,000 SNAs nationwide. The survey response represented a return of more than 12 per cent of the entire SNA workforce in school.
