First of all, let me say that I'm sorry to hear that you are STILL on dial-up
Reason for modem not knowing if it's connected or not depends on the driver (INF)...it seem to me that the drive is poorly written that's why it doesn't know connection has been lost (typically, modem drivers should do a connection check every 30 seconds).
My question is why are you stock with 33.6 modem...why not anything newer ?? I picked up 12 56 K V92 modem from computer depot (for developing purposes) for $36.....$3 per modem...I'm sure you can get you hands onto something newer then 33.6 for cheap.
Cheers