It looks like a faulty battery. It appears to be fully charged, but once it is fully loaded (during the call), voltage drops below minimum level required to maintain connection. Losing radio link afterwards is a clear indication of battery problem. What happens next, phone attempts to re-establish link to the tower, but it also requires transmitting radio waves and battery level drops again, phone is trying to find to the different tower, once it start transmitting requests, voltage drops again, etc....
Battery indicator might not pickup momentary voltage drop, as transmiting period is very short and battery voltage returns back immediately.
It is different effect to the worn battery, as worn battery can still supply sufficient current albeit of shorter period of time.
Try to remove oxidation of battery contacts with pencil eraser. If doesn't help, you can use any cheap phone R100 for testing.