Hi,
Try,
(1) checking COM port cable - could be a bad pin (if the modem is external), if that doesn't work use the other COM port
(2) in dial-up-networking right-click the connection and make sure the correct modem is dialing the number (if you have more than one installed modem)
(3) if its a PCI modem try installing it in another slot
Definitely since the problem is intermittent it sounds like a cable/connector problem (which may become worse over time).
Tell us how you get/got on
D.