First of all, thank you very much burnout426 for your very complete answer!!!
I have set to synchronize every 10 minutes these accounts.
Just to double check, you have 10 set in the text field for the setting, but do you have the checkbox for"check for new messages every..." checked? (I assume so, but asking just in case)
Yes, it is checked.
Does the log show that Opera is indeed checking every ten minutes. Do you see IDLE in the log?
I don't understand very well what you mean, however there isn't the word IDLE in the log.
Are you using imap-mail.outlook.com (port 993 with TLS checked) and smtp-mail.outlookc.om (port 587 with TLS checked)? There are (or were at least) some older live/hotmail IMAP server addresses that may be running an older IMAP server that you might want to avoid.
The parameters of the server are exactly those indicated by you. However the hotmail.it account is very old (about 5-6 years), while outlook.com account is new (about 2 weeks). Both are configurated as indicated by you.
Any anti-virus with an email scanner?
No. I have a classic Avira Free antivirus (the Mail Protection is not included).
Try double-checking in Thunderbird to make sure it's not messing up there too. Create a new outlook.com account just to test with and test that in Opera to make sure it's not just something with your account (sometimes can be).
Download the Opera Mail installer, launch it, click "options", set "install path" to a folder on your desktop, set "install for" to "Standalone Installation (USB)" and install. Set up the IMAP accounts in it (do not import) and see how things work fine there. If they work fine there, you should just be able rename your "mail" folder for your regular Opera (while it's closed of course), start Opera back up and add the IMAP accounts back in.
I use already a portable version of Opera Mail. However I will try to use a "new" Opera Mail with those accounts and a Thunderbird checking.
Is the time, date, time zone and daylight savings time settings on your OS correct? That can mess with secure connections if they're not correct.
Yes, it is all correct.
You might want to look at the log before the disconnect the server does to see what was happening before. In some rare cases, a single message in a folder can cause problems. But, usually you'll see the log stop at that point.
Mmmmhhh, I don't think so because my outlook.com account is new. There is only one mail in it: the classic welcome mail by Microsoft.
The force single connection option was necessary in the past for hotmail. I don't know if it's needed now with the outlook.com IMAP servers.
Nice, I understand. Thank you for clarification.
Thank you again for you help burnout426!!!