OK. Obviously the Rx is shutting down! Unfortunately I could not read the Rx volts during the problem as your hand was covering the Tx screen.
Do you have any electronics knowledge? The reason I ask is that I would try fitting a capacitor, (1000uf 10V) across the Rx voltage supply rail. This can be done by either soldering the capacitor to an old servo lead, a modified bind plug, or by jamming in into the rear of the pins of one of the servo leads where they plug into the Rx.
Some ESC/BECs have plenty of filtering on their outputs and some do not, (I suspect that price is the usual determining factor). The servos do have an input surge current and if the BEC has poor filtering and the Rx has no filtering then the surge can cause the 5 volts to spike. This spike can cause the Rx to enter Low voltage reset or some indeterminate operating area. In addition servos need a clean and stable supply or the positional feedback is upset and the servos will jerk and stutter, (sometimes even reverse rotation directional momentarily).
If you can try fitting a capacitor and see if the issue disappears!