With the per use billing model, instances are spun down after a 15 minute timeout to save you money. They then take a few seconds to be spun up when next accessed. It may be the Prestashop is timing out on these first requests (though I have no experience with that application).
Try changing your instance to a package billing, which has a 12 hour timeout, to see if this helps
https://developers.google.com/cloud-sql/faq#how_usage_calculated