Try dropping your connect speed by forcing a lower speed, if that stops the disconnect then line noise may be the problem. The second most common cause of disconnects is modem incompatibilities, again typically related to re-trains. Get the latest firmware revision for your modem. Every modem will be compatible with someone, but we have yet to see the modem that is compatible with everyone. As modems become faster they also become more complex.
Some modems have a way to record the reason why a connection failed.
If you can, try using an external version of another brand modem and see if the problems disappear. Another common cause of disconnects is line noise. Also unplug your laser printer from the AC wall outlet. We have learned that many telephone line 'surge protectors' or 'noise filters' will seriously impair your phone line. Do not route the phone line within three inches of any electrical cord or extension cord, or PC CPU cable, Printer cable, Monitor cable, any electrical appliance or power supply.