Agitation during fixing is mainly to do with making sure all the film has been reached evenly by the fix than getting fresh fix on the film all the time. You can demonstrate it by the normal method of testing if your fix needs replenishing. Put a spot of fix on an end of roll film leader and leave it for ten minutes, the spot will clear a patch on the film. Then drop the whole leader into a cup of fix and time how long it takes for the rest of the film to match the cleared spot. That time is doubled and that is your fixing time, longer than the manufacturer says and your fix is getting exhausted. But you will see that not agitating the fix still clears the film.

Steve