NO CARRIER signal returned from connection

Either you have a "noisy" line,
and the modem "hangs-up",
or you forgot to disable "call-waiting"
on the line, and somebody is dialing
your number, and the "call-waiting" noise
is interrupting the modem-to-modem communications,
and a "line-drop" is the result.

I have tried the suggestions so far, but recieve the same results.  When I use my modem online, I disable my call-waiting by dialing *70, then the ISP number.  As far as line noise is concerned, I think for the most part it is clean.  I do not hear any noise when I pick up the telephone reciever.  I can use the same modem with Windows 95 and have no problems staying connected.  I have another modem that responds the same way with both the windows (modem stays connected) and linux operating systems (modem doesn't stay connected).  What else can I do or try?

Check the command-reference for the modem.
Some modems respond to a given 'AT' command
by giving the "reason" for the disconnect.

So far, none of the suggestions work.  What else can I do or try?

Try "simple" hardware and software,
e.g. a copy of MS KERMIT running under MS DOS.
It will "hide" less of the "details",
and when the connection "drops", you'll be able
to "poke-around" to determine the reason for the disconnect.