Correct me if I am mistaken, but I am guessing when you loose a connection you are refering to the wireless connection between the modem and your computer and not your modem and the service provider.
So it probably has nothing to do with your Internet Service.
And you state that you have no problem with connecting to other wireless networks, so I would say there is nothing wrong with the wireless adapter in your computer.
You also say you have changed out the wireless modem from Qwest twice also, So the odds of you getting 3 bad modems with the exact same defect is really to high to consider.
So that only leaves your enviroment. Wireless networking works at 2.4Ghz. Unfortunatly that same set of frequencies it uses is used by other consumer wireless product, such as cordless and cell phones. There are many products that put out RF noise when being operated, such as microwave ovens, fans, A.C. Units, Portable Radios, Steroe Systems and even some Televisions.
So, to try and combat this RF interference try some of these simple things.
1) Place your router as high up as possible, RF from the router propagates like a umbrella. The higher it is placed, the larger the area it can cover with a signal.
2) Move all Cordless phone basestations, handsets and cell phones at least 5 feet away from the router and the computers wireless device.
3) Do not place the router or computer near any operating electrical devices like Microwave Ovens and Radios.
4) Your connection will also get worse the farther you move away from the router, especially if your home is made with alot of concrete or bricks. The only thing you can do there is to get a range extender device for your wireless network. You would mount it were the signal starts to get weak so it will amplify it for greater signal coverage of your home.
Hope that helps....