I installed the syslog-ng package on a test basis, set it to transmit on a remote port (24614), and interestingly enough, so far it's working without a problem 
Even when the internet goes down, I've noticed that it sends the packets in question, causing the continuity of the logs to be on the server.
Such strange magic, but the important thing is that it tends to work.
Thanx for info. Now I know, why I (still) prefere sysnlog-ng 
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Now I use it only too 
I changed the port for 1000 and still everything works
So it is your packet maangling in the network, not openwrt or syslog fault.
Correct, but it could also be rsyslog's fault, I don't have this problem with syslog-ng. In a few days I will try to receive logs on port 514 - if it works and the logs are written correctly, then it is only rsyslog's fault (I have not done anything to my network - I just installed syslog-ng, which is often used and recommended with OpenWRT (I just wanted to exclude the possibility that rsyslog is the problem, but it seems that with syslog-ng this problem does not exist).