If the mouths on screen move before the words arrive (or after), the drift is almost always introduced by buffering or processing delay somewhere in the signal path — not by your sound board.

Where the delay usually comes from

If it drifts progressively worse (not just offset, but widening)

That's a different problem — a clock sync issue between your video source and audio source, common with certain HDMI capture devices. Restarting the capture device/software usually resets it. If it recurs every service, note which capture card and check for a firmware update.

Quick check Test with a simple clap in front of a camera before service. If the clap sound matches the visual clap in your OBS preview, your local sync is fine and any drift viewers report is downstream (their device, their connection) — not yours.