The Taoiseach has now confirmed that schools will not reopen before September, with some reports saying creches for the children of non-essential workers may be among the last to open their doors. How can this possibly be rationalised?
Government ministers have said all along that they will act only on scientific advice, a significant part of which, in the case of schools, rests on the question of whether children can pass Covid-19 on to other people; so what exactly is the medical evidence regarding children's status as transmitters of infection?
The HSE continues to state that "children may play a big role in spreading the virus".
University College London is not so certain. Scientists there argue instead that the evidence for transmission by children is "very weak".
The research on which the HSE relies is contained in the Health Information and Quality Authority (HIQA) "evidence summary for spread of Covid-19 by children", published as far back as April 1.
It looked at two small family studies between December and March, and a mathematical model with a small sample size that had not been peer reviewed.
One of the studies centred on a single infant in China who was believed to have infected both parents, but details were scanty.
"The analysis of public disclosures data" in the examples studied "reported no cases of infection by an index patient 15 years of age or younger", and HIQA concluded that "there is currently limited information on how children contribute to the transmission or spread of Covid-19".
That is quite different from the HSE's assertion that children may "play a big role" in spreading Covid-19.
At the start of the crisis it was decided, reasonably enough, that it was safer to keep schools closed. But the data has evolved considerably in the intervening weeks. As the HSE acknowledges, "coronavirus is a new virus" and "we are still learning about it".
There doesn't appear, though, to be any indication that further research is either being conducted or analysed to shape advice on schools to help parents back to work.
It's certainly true that children are far less likely to transmit Covid-19 to adults than the other way round. That's because they tend to be asymptomatic, and therefore cough and sneeze less frequently, according to the World Health Organisation (WHO); but that doesn't mean they can't transmit it at all.
A new study by Berlin's Institute of Virology argues that they may indeed be as infectious as adults, and public health experts in Germany are not yet recommending widescale reopening of schools and kindergartens.
But that doesn't seem to chime with the other evidence. Experts who worked on the WHO's China joint mission report could not recall any incidents of child-to-adult transmission.
A separate study by the Dutch National Institute for Public Health and the Environment, which collated information from GP surgeries and testing centres across the Netherlands, also couldn't find a single example of a child infecting another patient, not even elderly relatives with underlying health conditions, and concluded that "children play a small role in the spread of the novel coronavirus".
If nothing else, that suggests there may be little scientific basis to keeping children away from their grandparents until June, the latest timeline laid down on Friday.
In France, a study of the early Alps cluster also came to the same conclusion. One child even failed to pass on his infection to a single other person despite having more than 170 close contacts in three separate schools.
Again the conclusion was that, because the virus is so mild in children, they're less able to transmit it.
Australian research likewise found that Covid-19 had reached only 15 of the 3,000 schools in New South Wales. Doctors were surprised because of the known role of children as "superspreaders" of other diseases such as flu. It suggested children could be "dead ends" for the virus. They catch it, but don't spread it to anyone else. So why keep them locked up at all?
Most attention last week was given to a review of 78 available studies by the UK's Royal College of Paediatrics and Child Health - which again found no evidence whatsoever of transmission from a child under 10 to anyone else.
One of the authors of that report has denied that this means children cannot transmit the disease, pointing out that an absence of evidence is not evidence in itself.
Nonetheless, many epidemiologists are coming to the view that the spread of the virus is best managed with schools remaining open rather than closed, as long as social distancing and hand-washing remain in place.
Of course, there are other considerations besides the narrow question of whether children can transmit Covid-19. That includes a worry that reopening schools would increase the numbers of adults travelling to and fro outside the home, who may then interact. But there are known risks from keeping them closed, too.
One study by Indian paediatricians repeated the warning that "the most significant threat to global child health... is unlikely to be related to Covid-19, but rather the socio-economic consequences of a prolonged pandemic".
That matters hugely, too.
Even if it's not considered right yet to reopen schools, surely there's no basis anymore to stop younger children mixing with one another?
Yet another study of more than 9,000 subjects, this time from Iceland, one of the best countries in the world at containing Covid-19, determined that young children were largely unaffected, and that "going to school and playing outside is therefore possible", while continuing to advise no contact "between parents".
On what basis have creches been pencilled in as the last to reopen - and even then only a limited basis? Parents need childcare to return to work.
The conversation is moving fast elsewhere, but Ireland seems to be lagging behind the science. The most recent letter from the Department of Education and Skills to principals and teachers is dated March 25, and continues to stress the need to "convey to students the absolute need to practise social distancing, and to minimise physical contact with each other, to help avoid the spread of Covid-19".
That included advice "to avoid meeting up". Given how we know young people's mental health outcomes are harmed by prolonged social isolation, that seems unjust, but the government appears unable or unwilling to factor it into their calculations.
We're asking a lot of them in the lockdown, and the sacrifices they're making should be based on the best available scientific evidence, not outdated assumptions. Students and parents deserve no less.