Im not familiar with that model of router, but the problem seems familiar to something i've seen once before. Basically the dgn3500 is tripping out when there are to many clients connected wirelessly using 802.11n (150-300mb connection speeds).
It seems to draw to much power in the high speed modes with lots of wireless clients. What I ended up doing was switching it to 802.11g (54mb).
Maybe its whats happening with you, ask who ever has access to the router to downgrade the wifi to 802.11g (54mb) and see if the problem continues
A mate got a Belkin that does the same thing, i wonder if that have the same problem? He don't use it now as it was causing all sorts of problems with not allowing him to acess some sites and not allowing windows to update, I tried all ways, opening ports on the belkin, but gave up.
Anyway he had the problem that when someone else tried to connect the router would reset.
He got a old Netgear 834 just normal ADSL and it does a better job than the up to date Belkin.
Desktop machine now powered by windows 7 pro 64bit , laptop by ubuntu
On ADSL24 using C&W network.