we have some occassional problems too. As for me, I don't believe in AMD myth. We changed completly two PCs, various parts, and sometimes system locked on us - still the same scenario - refusing Winbox, refusing SSH, Internet connection still running for some time.
As for me, I would not run ANY important site without external GSM or ping watchdog.
PS1: - on Czech MT forum, there is one interesting post. Some guy was exchnaging PCs too, various components, still not luck. Later on, with one consultant, they found some dependency. The faulty part was Compact Flash card - maybe it becomes corrupt from time to time. When he used binary backup, there was some trouble. So after your new HW installation, try NOT to use binary backup, but import exported plain text configs, it might help ...
PS2: two weeks ago I was at another MT training here, and guys were suggesting SuperMicro boards. Those are reported as running absolutly flawlesly. SuperMicro are server class boards, they have multiple PCI busmasters etc. A bit pricey, but maybe worth it. But I am not really sure the trouble lays in proper HW. Isn't there Linux underneath after all? I doubt AMD processors are insufficiently supported, even with old 2.4 kernel, which current ROS seems to be based upon ...