have they checkedc for minor strokes because my grandfather was a drinker so we always thout his stumbling and falling to one slide and sometimes slurred talking was due to alchohol but unfortunatly he didn't believe in dr.'s but it was determined that he had atleast 8 minor strokes that caused that behavior and unfortunately died of a sudden heart attack. So keep getting different opinions from different Doctors & sopecialist.
He could be having TIA's. He needs to be seen by a doctor. A cardiologist.
I would talk to a doctor about it, preferably a neurologist. If he keeps falling to the same side, it could be one-sided weakness, which can be caused by things like strokes or subdural hematomas. Did he fall and hit his head any time in the last year? Sometimes blood can collect very slowly in your head after a fall and take a couple of months to show slight symptoms (happened to my grandfather). Especially if you have insurance, please take him to a doctor soon in case it is something serious.