I am no expert but have been through what you are going through. From what you say I suspect your line is dirty. You may have already checked this? If you connect sometimes and stay up and not others then the way your calls are being routed is being directed through a dirty exchange.
Put a phone on the line and dial up the number and listen. Not to the ring or the modem on the other end but the line clarity. If you hear pops and clicks and bleedover that is your problem. Do it several times since your call can be routed different. If that is the case call the phone company and tell them you have a noisy line. You don't have to tell them you are running electronic components if you don't want to.
It is up to them to provide you with a clean line up to your box and there shouldn't be any charge for them to do that. I would also check from the box in to the modem and that is your responsibility. Make sure connections are clean and protected. I keep my box clean and well sealed using silicon around the wire inlets to keep the insects and moisture out.
When I went to ISDN (they use the same wires) they took months to install they kept reporting technical problems. I finally caught the install man. He said the problem was their box was full and they didn't have a clean enough line to put ISDN on. I told him to take one of my other 4 lines. He couldn't find a good one out of the 4. He finally swapped pairs with someone elses and gave them one of my dirty pairs. No wonder I had problems with my modem connection. While it worked most of the time when it rained etc I had disconnect problems like you describe.
I would be happy to help you as much as I can. You can call me voice in the evenings if you like at 901-759-1541 between 7-9pm Memphis time. I used Supra's and can help you with settings files on them. I also used FreePPP which allows you to run an application after connecting and I used it to run a startup script.
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