I've been trying to figure out something very similar that I've been
experiencing. There's one land line that I call frequently from my
T-Mobile phone that will just immediately drop the call instead of
giving me a busy signal if they are on the phone; my phone just hangs
up without ringing or giving a busy signal. If I call the number from
another land line, I hear a busy signal. My T-Mobile phone does get
busy signals on other land lines that don't have call-waiting, so it
seems to be dependent on the combination of my T-Mobile phone and this
specific land line.

The first few times my cell phone just disconnected, I just assumed
there was something wrong with the other person's phone, but later
learned it was because they were using the phone. At least now I know
why my phone was disconnecting and it hasn't really been bothersome
enough to ask customer service about it. (Dealing with customer service
might prove to be more bothersome).

David