iPhone keeps losing signal right after picking up a call
In order of my preference to get things fixed, you'll likely need help from someone else to tell which.


The battery is failing and can't provide the extra power once the call comes in. The radio may be fine at idle listening, but when you call it could need to boost power to get the signal to the tower for transmission from the phone to the tower.
The phone is on an overloaded cell tower and once the call is connected - the cell tower wants to hand off your active call to a less loaded tower that has different distance / signal strength. (The overload would be non-idle lines - towers can handle many devices that are idle - but need to hand off active transmitters and downloaders when bandwidth caps are reached.)
There's something about that specific radio where the tower is cutting the calls short.
All of the above might be summarized as "call the carrier" in question for more help


The battery might be diagnosed by Apple or you might need the carrier to see the transmit power on your phone when this happens. The cell tower shift would also need the carrier to help. I suppose field test mode might work as well to help diagnose this, but I'd start with the carrier first. The last is 100% the carrier that needs to look over the patterns of disconnect. They surely can trace why 5 calls all drop from one piece of gear if you ask.