I'm not a phone technician, but I am a technician who works with low voltage lighting control systems.
Anyway, the answer you seek is easy to find. It's simply a process of elimination.
First I would eliminate all inside wiring from the equation by connecting at the point of entry (as you explained you already have), when doing this though, make sure you also disconnect any wires downstream (going into the house). I would try to keep the patch cord (your temp phone cord) as short as possible and make sure you don't run the wiring along side any line-voltage (household power) wires or TV signal wires (coax).
Actually, this is something I suspect, based on what you described, but I'll come back to it a little further down.
This should go without saying but, don't use any of the cords that you normally use when you experience this problem. Buy a new cord if you have to, or borrow one from someone. Make sure to use your DSL line filter (and be sure you have it hooked up correctly).
If the symptom is still there at this point, then you're almost done with your part. Now here's where the not being a phone tech part comes in. I'm not sure if Ring&Tip polarity need to be observed in this case (maybe someone who knows the answer will chime in), but you can be sure to rule that out too by simply swapping the two wires and testing again.
Now you just need to rule out your telephone as part of the problem. Simple, borrow another phone (just a basic phone) plug that into your filtered line and see if you can recieve a call without dropping your connection. If the symptom is still there at this point then you know it's either the modem itself or the problem resides upstream of your house. Either way, you can call a technician knowing that you shouldn't be charged.
Be careful to pay attention to the tech because sometimes the tech will twist things to make it look like it's your fault when he knows it's not the truth. If you let them, they will charge you. And DON'T LET HIM LEAVE before you test to be certain the problem is gone. If he says there's nothing he can do about it, make sure he writes exactly why in the work order.
Now, back to the thing from above. If the problem went away when you removed the inside wiring from the equation (as described above), then you need to check a few things. First, make sure your phone wire is PHONE WIRE preferably Cat.3 or Cat.5 (twisted pair cabling), what I mean is that speaker wire, extension power cords, 12ga solid, flat phone cords (like the kind that connect your phone to the wall) are not acceptable as inner wall phone wiring. Also, (assuming you have only one phone number) make sure you have only one (1) pair of wires (either [a Blue and a White-Blue Striped] OR [a Red and a Green] depending on the type of wire) being used for your entire house.
This is important--DO NOT CONNECT UNUSED PAIRS ATTEMPTING TO DOUBLE UP ON THE COPPER! Phones don't work the same way light bulbs do, meaning two wires is what it wants, and all it needs. Any more than two wires is going to make havoc for any type of digital signal. I'm not going to explain why cause I don't really enjoy typing, but trust me on this. Just run one pair to the first jack and then go from the first jack to the second jack with one pair. DO NOT use two pairs in the same cable jacket for two jacks sharing the same phone number. Do not use the extra wires for anything else such as doorbell, radio antenna, alarm wire, plastic explosive detonator, trip-wire to a home-made claymore, etc.
The reason I'm stressing all of this is because this happens to be a forum for speed hungry tweekers, and so it occurred to me that you might have "improved" something you haven't mentioned. Regardless of which definition of speed you think I'm referring to nor which type of tweeker you might be...the same applies to any and all.
The stereotype I'm referring to is the tendancy to s00p-up things with out always having the patience to learn how to do it correctly. You know, like taking the air filter out of your car to make it go faster (less air-flow restriction, right?), only not realizing that the engine management computer will see this as a failed sensor condition and put the car into limp mode (as in limp home vs. not work at all) where the air/fuel mixture isn't optimized at all, but rather rich enough that the car can be driven without being damaged...much.
Well, using spare wires for doubling up copper fits the same profile. More copper isn't always better. C'mon, just own up to it. I bet that profile fits 9 out of 10 in here. It's okay, I've been there. Here, 10bux says that your DSL modem already has the tamper-seal broken and the tamper-proof screws already removed. LOL! Sorry, I just have a weird sense of humor. But I crack myself up!
So back to the subject:
It's equally important, that your phone wire isn't routed along side any sources of noise (electrical noise--not audible noise). Such sources are A/C power wires (to recepticles and light switches/fixtures etc.), transformers, A/C motors, cable/satellite TV, doorbell wires, etc. It's okay if the phone cord crosses over a piece of Romex carrying 120Volts here and there but they should not be routed side by side for longer than a foot or so. They should NEVER share the same conduit (pipe).
Okay, thats all I can think of. I trust you will let us know the outcome?