Since ammonia and nitrite readings were zero, I may assume the tank is cycled? If so, the oxidation of the ammonia and nitrite into nitrate is what causes pH to lower. Ammonia has no charge, but both nitrite and nitrate have negative charges -- increasing the concentration of H+ ions, thereby making the water more acidic.
In order to prevent this, the results of a GH or even better a KH test would be handy. GH will give you a general idea, and KH will give you a good idea of how much buffering capability your water has. Where buffering is most simply the ability of your water to keep its pH constant.
Otherwise, more frequent water changes will help replenish your water's natural buffering capability. If you do not want to do a large a water change every time, that is fine, but smaller volume but more frequent water changes will help the water naturally. You may also consider looking into baking soda, but I have not had experience with that (my pH and hardness are more than adequate!). Otherwise, if your pH is 6.8, a commercial buffer designed to work at 7.0 might also bring you the stability you want. But, since most of us prefer not to add chemicals if at all possible, I would try the increased water changes first. So long as you condition the water, match the temp, hardness, and pH as close as possible, and you do not disrupt too severly your beneficial bacteria, you can do almost as many and as frequent water changes as you like.
