Mails not downloaded after import accounts from Thunderbird

I imported all my mails and accounts automatically from Thunderbird into Postbox, and settings and old mails all seems to have been imported correctly. However no new mails are downloaded to my accounts (all are POP3 accounts using Gmail as the mails service), and I do not get any error message. Nothing is blocked in my firewall.

Any ideas of what I should try to get past this would be very welcome!