With the newest revelation thanks to mor_mot on the Shadowblade glitch, the way we look at stats have changed.
mor_mot discovered that stats (with the exception of HP/TP) do not change when a character levels up until a character's equipment is checked, their status screen is seen (?), or the Order command is used to change party order. This is used so that the Shadowblade strats can be used late into the game.
That being said, whether you use Shadowblade strats or not, this holds true for every character. When a character levels, if you do not do one of the previously mentioned menu commands, you are losing out on valuable stats that could possibly RIP a run, especially Agility and Mental (which affect Defense and MDefense respectively).
So when you're in a run, just do yourself a favor and give each character a quick look over or change their order.