I'll give away some of my tricks here...
Make sure that you don't have any bridge taps on your wire in the run for the pair used by the DSL. If you do, you might try to remove them. I've seen that cause DSL issues (sometimes, not always). I would filter the DSL in the demarc, not send the DSL to any extensions/phones/etc on the other end and rely on remote filters. Filter it once at the demarc (assuming this line also has dialtone).
If the DSL is provided by a telco (not in-house), are you sure the exact modem you are using is approved for this specific customer by the telco (one telco might support multiple modems, none of which would work for *every* customer, as it depends on CO equipment too)? I've seen for instance Cisco routers with DSL WICs fail to be stable on certain models of (ironically) Cisco DSLAMs - swapping the Cisco router out for a different model or getting the telco to move the line to a different DSLAM often cleared up the issues. If they provided the modem, than this isn't probably the issue (although I've still had some problems solved by changing CO DSLAMs).
The first step I do in troubleshooting this is to verify that I have the same issue at the demarc, without being on any building wiring. If it doesn't work there, it's the telco's problem (assuming the customer is using an approved modem and you've tested another modem which also failed).
I also would disconnect any phones and filters from the wiring - go straight from the demarc to the modem (no phones at all). If you have an unbalanced wire plugged into the filter (an open wire somewhere), even if it is "downstream" of the filter, it can cause issues.
Another trick I've dealt with when the modem won't stay connected and I know the wiring is good is to order a new line (without disconnecting the first until the new one is in) - that forces a different pair back to the DSLAM, and any problem in that pair will now be irrelevant. Of course that costs money (less than an hour of a tech's time, though). I usually use a fax line if one is already there (less likely to get "messed" with and will be less missed most of the time if I need to get to the line to troubleshoot). If I disconnect a fax machine for 10 minutes, most organizations handle that better than if I disconnect one of their incoming voice lines for 10 minutes!
If you truly think it is the air core cable, move over to a different pair - see if the problem follows. Sometimes it's easier to fix the problem than find it.
