The second most common cause of disconnects is modem incompatibilites, again typically related to re-trains. Many other brands have upgrades as well, these are well worth it. 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. Make sure your modem register settings do not restrict its ability to adapt to phone line conditions.
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. 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. Inductance from electrical lines and radio transmitters wreaks havoc with phone lines.