Reasons For Router Randomly Rebooting?

[The Knome]

Like the title says, at times the ADSL router will randomly reboot.

So far to try and suss the problem I have:
Tested 3 different routers with all doing the same.
Replaced the cable to the modem with a Cat6 shielded.
Replaced the microfilters.
Check the phone wiring my side (within the realms I am legally allowed to do).
Checked and updated the firmware on the router.
Checked and updated the firmware on the PC for the networking adaptor (just in case, being built in).
Checked every other cable I can muster.
Checked the current and voltage on the mains in case is was some kind of surge.

Been on the phone with the ISP who checked their own modem and called it dead, which has been confirmed after all this work (but borrowed and a new router with the exact same symptoms? minus the refusing to connect at all aspect).

At the moment, got an old spare wireless network card in the main desktop to see if it stabilises, but with the randomness its going to be tricky, as some days its been perfect, no drops at all and other times like last night it just rebooted every few minutes.

EDIT, same result regardless of being on wired, or wireless connection.

At a bit of a loss and looking for any other input from the tech community?

Before I go calling in an engineer to check their side of the wiring want to make sure I have crossed off any, and all possibilities on my end. 

[paddy-stone]

I had a similar problem one time... in my case I got the ISP to send an engineer as I knew there was no problem my end. It turned out to be the faceplate where the outside line connects, the connections inside had been melted a bit by a power surge when there was a lightning strike nearby that took out some other ISP equipment. I only knew this as the engineer that was sent was the same one that had to deal with the other ISP equipment a few days earlier.

It may not be the case with your problem, but if you've checked everything else reasonably required at your end then I think an engineer visit is the next logical step. Good luck.