have you tried a different power socket, if possible run an extension from a socket that you know works 24/7 without issue such as one with your pc on/ tv/video etc? also, when you changeed routers, did you use the correct power supplies/adapters that came with them and not anything else?
. I can connect to the Internet if I let the router sync and connect without the Ethernet/USB cables plugged in, but if I leave them in whilst it is trying to establish a connection... the same reset cycle occurs for hours. Now, normally this would just scream that the router is broken... but how is it broken if it can hold a connection perfectly for 24 hours-- coincedentally at the same time that an engineer performs work on my line?