Yes, finally I have figured the problem out.
When I noticed the ADSL router disconnecting from the ISP even though it was not plugged into the ASUS router at all - something clicked in my mind and indicated that I had been digging in the wrong direction...
As it often happens, the problem has turned out to be much simplier than it appeared to be.
It was bloody generic USB hard drive connected to the device. Apparently every now and then when the HD was being accessed, it was creating some noise (interference) and the ADSL router was picking it up.
So I changed the hard drive enclosure to a more expensive one (seagate) and finally my problem is sorted out (knock on woods...)
I can now copy files accross from the ASUS router and at the same time surf the Internet comfortably. Though the router is now is configured only as a WiFi access-point and torrent downloader.
Possibly will configure the router back as a full-blown router to enable wshaper when I have time, but not now. I'm quite happy with the way things are at the moment.
Thanks everyone for the help.