I can't count the number of times this has happened to me. Any time I spend a lot of time on the phone with AC, the call eventually gets disconnected and they NEVER call back. Just happened after spending 30-40 mins on the phone with AC agent to modify a ticket (most of the time I was on hold while she was checking things). I was ready to make the payment for the change fee and air fare difference (only $136) and I wanted to use a $100 gift card plus credit card for the balance. Agent put me on hold to check with technical support, then disconnected me.
I have spent hours on the phone with UA over the last several years. I cannot think of a single instance where I have been disconnected.
Even Expedia always asks for your number in case the call gets disconnected. So low class AC!