Sounds like an overheating problem but you say it happens after one minute, is this one minute from a previous reboot or from a cold start-up?. A lot of chips have thermal shutdown protection and they will restart. Does the unit have good ventilation?
Also, have you updated the firmware recently? I saw a Belkin ADSL wireless router a couple of months ago that was new out of the box with a firmware from 2004.
I am assuming that you have security turned on, otherwise it could be a neigbour having a bit of fun!
Good luck
Dale