I've just discovered, with the help of Uwe Kein, who suggested me to use Process Monitor to see if there was any problems with permissions that, in fact, the log file was NEVER even accessed. This started me wondering why... And I just realized that the HttpModule which was the source of the NSec logger was not running at all, so, in fact, no log was actually ever being made.
This problem occurred because the web.config on the destination machine wasn't successfully updated in previous deployments, so the HttpModule was configured the IIS6 way... I had to add it to the modules section as shown in: https://stackoverflow.com/a/2935410/285678
What is great about it was that I've just added this log to try to find the reason why this HttpModule was not behaving as expected, so finding out why NLog was "not working" resolved this issue (which was a very serious issue, as the HttpModule pertained to the security system of the application!)
I've tried to close the question since it is misleading, as it is not an NLog error at all, but it needs 50 votes to be closed! So I'll left it as a warning to people like me who, in desperation, ask "not very wise" questions in StackOverflow :-(