Too little information to really help you out OP.
a) you are aware of the ports that XBOX needs opened on your end, right? If not,
here they are againCorollary of this would be to use something like GRC Shields Up to test whether the above port(s) are open and
listening from the outside or not.
b) what equipment is present -- you mentioned a "modem." What make / model? Who is the ISP? Cable/DSL? Any
equipment behind the "modem"?
c) when / why do you have to reset the modem? Is it related directly with your XBOX issues? Or something else?
My inital thoughts.
Regards