Have data recorded during period when target phone has no internet connection been lost?

No. When the target device does not have an internet connection, TheTruthSpy still records data but can not send data to the server. TheTruthSpy will save all recorded data in temporary files on the target device and wait to send again when the target device has an internet connection. Therefore, the recorded data will not be lost. But you have to wait until the target device has an internet connection to review new data.