If I have a 'Potion of Weakness' and 8 or more arrows in my inventory, I get a visual showing that I do not have the potion, although it is clearly in my inventory.

The only explanation I can imagine is that, if there is a difference in the duration of the potion I have (i.e., 4:00) and the duration of the potion on the crafting table, perhaps I am not considered to have that potion.

However, that would suggest that there is some other way of acquiring potions of the appropriate duration, matching what the crafting table permits. That would seem counter-intuitive and very user-unfriendly.