After a further analysis, it has been evaluated that the error message displayed to the user to inform about wrong permissions should be enough for letting administrtors fix the problem by changing permissions manually and in accordance with their security policies. Fixing permissions automatically could instead not being compliant with company security policies. 

Steps to reproduce:

1. Create the nxlog directory with full permissions and the nx user as owner
2. Enter a path to the folder in key CommonLogDirectory in node.cfg file
3. Restart nxserver using command: 

sudo service nxserver restart

As a result, connection to that host is no longer possible due to wrong permissions being assigned to the newly created server.log file:
-rw------- 1 nx      nx    nxserver.log

In some cases, the nxnode service is also disabled.

As a workaround, remove server.log and then restart nxserver:

sudo rm /var/tmp/nxlog/server.log
sudo /etc/NX/nxserver --restart

In that case permissions to server.log file are assigned correctly:
-rw-rw--w- 1 nx        root      server.log