Our troubles have been accompanied with «Unusual Paypal Activity» emails.
Thus, we tried to fix the problem like described here: viewtopic.php?t=8356&f=3#p32736
Directly from the course we have failed to use the proper fix and have decided as a temporary to use easy fix.
Immediately transactions have begun completed properly in both PayPal and OJS sides.
A little later (about an hour) problem arose again, but now verifying of any peer certifcates is already turned off!!!
So far we do not know what to do, think...