OK. Are these IMAP accounts all with the same provider? If you can set up a free account with another provider and test an IMAP account with it, maybe it'll work for that one and then we can see what's up with your regular ones.
No, of different. I also thought about that But they behave exactly the same.
How do you have your taskbar configured? Anything different than default with your systray icons?
No, standard configuration. And I changed nothing at all - just made IMAP accounts.
What OS?
Win 7 64x. I also use Avast Free Antivirus but I tried to turn it off completely - no changes.
But, if you're done messing around, I'd just use Thunderbird.
I thought about that. For the last week I tried: Mailbird, Postbox, eM Client, Mozilla Thunderbird - but I didn't like them.
Mailbird and eM Client are great (though they cost some money) but they do not have RSS-reader. Mozilla Thunderbird has RSS reader but this program looks totally different than Opera Mail. i tried to work with it but... I can't. I so got used to Opera Mail that I think it is the most comfortable, effective and simple client in the world. Can you imagine how upset I am? Today I will install Outlook 2013 - may be it will be good.
By the way, if Opera Mail takes about 70-80Mb of system memory, Mailbird and eM Client take 130-150 and even more Mb ((