Are you sure it is the modem portion and not the router or the wireless access point portion of the device?
The problem with ADSL modem/wireless routers are that they are four devices combined into one. They are a modem, router, switch and access point, all connected with internal wiring. This makes it a bit more difficult to troubleshoot exactly where the problem lies.
The first step is always check layer 1. Swap out cables, test with different NICs, different computers, different ports, different channels, etc.
Then you need to direct connect a computer using a cable and test ping to the primary DNS for a few hours. Look for packet loss, latency, jitter, etc. If you see problem, call your ISP and have them do a loop test (it is always best to call WHILE the problem is occurring and BEFORE you restart your equipment).
If you see a problem there, then you might try syncing at the NID. Take the modem out to the phone box, sync up there and run the same tests. Your ISP will want you to do this anyway as it rules out your building's wiring (a very common cause for issues).
If you still see problems there, the ISP will have to figure out what is going on (maybe your loop was extended, or you have some issues with margins that are being caused by a bad modem, voltage on the line, grounding, bridge taps, etc), but they'll be able to test for all that.
If you see no problems during those tests, then it is likely the router or access point. Connect two computers, when one goes out, see if the other still has access (in most cases, the wireless loses access, but the wired is fine). This indicates a problem with the wireless. If it is the other way around, the built in switch might be bad, or the router itself is having issues.