The best strategy here is to calibrate at the beginning of the session (using the normal idea of an experimental session, referring to the overall visit for the day), and then then check the validity of the calibration between trials (i.e. with multiple trials making up your session).
Only actually re-calibrate if the calibration no longer appears to be valid. Calibrating too often can itself lead to problems: only re-do it if it is actually necessary.
Ideally record the calibration checks so you have an objective record of the calibration quality throughout the session (e.g. before each trial, show some stimuli at a succession of known locations and have the subject fixate each in true). This means that each trial of recorded data has an associated record of the calibration quality.