Telekinesis enables you to move an object up to 30ft in any direction, including upward. Once I have lifted the object up, on subsequent rounds do I need to use my action to keep it in the air?
I can see the argument for both sides, which I set out in 1. and 2. below.
No, you only need to use your action on subsequent rounds if you want to move the object further.
With regard to creatures, the spell (PHB, pp. 280-281) states that:
A creature lifted upward is suspended in mid-air.
Presumably an object lifted upward is also thus suspended. The spell states that:
When you cast the spell, and as your action each round for the duration, you can exert your will on one creature or object that you can see within range, causing the appropriate effect below.
The 'appropriate effect' it specifies below for objects is that you can move them up to 30ft in any direction. So you ought only to need to use your action on subsequent rounds to move the object, not to keep it in the same place. As long as you maintain concentration, you still have a telekinetic grip on the object, keeping it in the air.
Yes, you need to use your action on subsequent rounds to keep it in the air.
The spell does not state that when you move an object with Telekinesis, it will remain in the same place even if other forces are exerted on it. Telekinetically moving an object that is worn or carried requires me to make a contested roll against the creature's strength check:
If the object is worn or carried by a creature, you must make an ability check with your spellcasting ability contested by that creature's Strength check.
This assumes that my telekinetic grip is competing with other physical forces acting on the object. So if I telekinetically move an object somewhere where a physical force is exerted on it, then I would need to use my action if I wanted to prevent it being moved by that force on subsequent rounds. For example, if I telekinetically place an object inside a moving vehicle, it will move with that vehicle unless I use my action to exert my will over it to keep it still or move it somewhere else. Gravity is a physical force like any other, and in the absence of any countervailing force it will move an object downwards. So if I want to lift an object into the air, and then keep it there on subsequent rounds, I need to take my action on each of those rounds to manipulate the object to stay in the air.
I am not sure which of these interpretations is correct. Any help would be appreciated.