I would FIRST try capturing for an hour from some OTHER source to establish WHERE the problem is. Since the audio and video are literally, physically locked together on the tape, I can’t see how that could be the problem, or how using an external sync generator would have any affect at all on this problem.
Do you have any other long-form capture experience with this Decklink card? There have been several infamous examples of computer interfaces that had problems with long-form audio/video sync. The problem was the design of the interface card. The audio and video sampling are, by necessity, done by separate circuits, and their rates are not locked to each other. Not a particular problem for short clips, but too much drift for long-form.