It comes after the Scottish Government expanded the definition of key workers during the winter lockdown.
Rockfield Primary School reported a surge in demand from 20 in last year's lockdown to 80 this time.
And now the 136-pupil St Columba's RC Primary School has confirmed it too had seen increased demand with inquiries for places up from just three last year to nearly 30.
Shona Fox, chairperson of its Parent Council, told The Oban Times: 'We would just like to reiterate what Rockfield has said and ensure that people understand that the virus is more transmissible this time so people are more likely to catch it.
'Therefore, it is crucial that only people who have absolutely no other alternative childcare should send their children to the hub.'
She added: 'We would ask employers to be as flexible as they possibly can be with regards to working patterns and enabling people to work from home to keep the number of people coming into contact with each other to an absolute minimum.
'This, in turn, will reduce the period of time we need to be in lockdown and enable us to get our children back to school, safely and as quickly as possible, which is what we all want.'
She thanked teachers and staff of St Columba's Primary school for continuing to go 'above and beyond' for pupils and said it was greatly appreciated.
'We would also like to extend our thanks to all the kitchen staff, janitors and cleaners at Oban Primary Campus, who also contribute to our pupils wellbeing,' she said.
The issue has been raised with ministers with some MSPs saying it had caused 'confusion' over key workers and that greater clarity was needed.
Addressing the issue, John Swinney MSP, cabinet secretary for education and deputy First Minister at the Scottish Government, said the category had been expanded to include those 'upon which the functioning of the Scottish economy is critical'.
He said flexibility had been left with local authorities to apply the guidance more specifically to their local area because different parts of Scotland were more dependent on certain sectors.
But he stressed: 'We must keep to a minimum the number of key worker children that present at school because only by that mechanism can we contribute to the national effort to reduce human interaction and therefore stop the circulation of the virus.'
'I'm mindful that working parents of very young children are finding it particularly difficult to balance childcare and work at the present moment.'
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