Certain aspects and embodiments of the present invention are directed to a semi-autonomous insert valve. The semi-autonomous insert valve includes a body, a closure mechanism coupled to the body, an autonomous actuation mechanism coupled to the body, and a control system disposed in the body. The body engages an inner wall of a subsurface safety valve and causes a subsurface safety valve closure mechanism to open, allowing fluid to flow toward the surface of the wellbore. The closure mechanism selectively allows fluid to flow toward the surface of the wellbore. The autonomous actuation mechanism actuates the closure mechanism independently from a subsurface safety valve actuation mechanism that actuates the subsurface safety valve closure mechanism. The control sub-system includes one or more transceiving devices that can wirelessly communicate signals. The control sub-system closes the closure mechanism in response to losing signal communication between the transceiving devices and a signal source.