Unfortunately, you can try everything with a SM56 without great success.
In a conclusion:
1) If you are with XP, take the Win 2000 version, it's the better.
2) You can look for an Motorola V.34 init string. I work for an ISP and some people can stay two or three times longer on Internet before they'll lost the connection. (But you must accept the sacrifice to lost 1 or 2 kB/sec.)
3) You can try to "ping" continuously but lightly a fixed server because the SM56.
4) If you have a long phone cable, you can isolate it or reduce it to less than 3 meters.
The best solution, it's to buy an other BRANDED modem, like a 3Com, or to buy an old but very stable 33,600 bps modem.