There is more water in it than the air can take away
CommonRoyal icing has no cooking stage and no crystallisation to manage: it hardens because water evaporates and leaves a rigid sugar matrix behind. Anything that adds water — extra egg white, liquid colouring, a wetter flood consistency — has to leave again before the icing is set, and anything that slows evaporation has the same effect as adding water. Sugar is hygroscopic, so in genuinely damp air the icing can reach equilibrium still soft and stay there indefinitely. That is why the same recipe sets in an hour in February and not at all on a wet August afternoon.
What to change
Change the room, not the recipe
Move the work somewhere dry and get air across it — a fan on a low setting, an open window on a dry day, or a dehumidifier if this is a regular problem. Stiffen the icing by adding icing sugar rather than by beating it longer, which incorporates air and makes it more fragile rather than drier. Use gel or powder colours instead of liquid ones, because a liquid colour is mostly water and all of it has to leave.
Any royal icing that is soft, tacky, or still not set after several hours. Not applicable to a batch containing a deliberate quantity of glycerine, which is not going to harden and is not supposed to.
Trade-off: Faster drying gives a harder, more brittle finish, and a very dry room can crack fine piped work as it sets.