Hi,
Since this is a DSL modem I would make sure that your line is clear. Have the ISP do a line check and be sure to check all the filters connected to all phones within the line area. Bad filters can cause this type of issue.
Another thing would be sure to have a good AC source, check the socket or check what is used on that same circuit that could create power line signal injection (motors, refrigerators or any large on/off system). If you do not have experience working with electrical then have a qualified person do the checks.
You could use a UPS for the modem to insure the problem is not due to drop/brown/noise on the AC line that can cause outage or a intermittent power issue(noise, power drop/changes). You can get the small UPS designed for modems for around $30 US.
Intermittent problems can be very hard to track or diagnose.
Hope this helps.