The Mysteries of Aaron Reed's Remembering Extension (and a solution)

I think the following covers your intended cases, and it’s not difficult to add in the functionality to indicate where something was last seen.

Unavailable Things
"Unavailable Things"

[Doesn't use Remembering because you said your actual goal was simpler.]
Include Epistemology by Eric Eve. [for "seen"]

Place is a room.

Other Place is east of Place.

A red ball is in Place.

An open openable container called a box is in Place.

A blue ball is in Other Place.

[An alternative to scope testing via direct object tree inspection]
To decide whether (X - thing) has line of sight to (Y - thing):
	let CA be the common ancestor of X with Y;
	if CA is nothing, decide no;
	let checked be an object;
	now checked is X;
	while checked is not CA:
		now checked is the holder of checked;
		if checked is a closed opaque container, decide no;
	now checked is Y;
	while checked is not CA:
		now checked is the holder of checked;
		if checked is a closed opaque container, decide no;
	decide yes.

To decide whether (X - thing) does not have line of sight to (Y - thing):
	if X has line of sight to Y:
		decide no;
	otherwise:
		decide yes.

Definition: a thing is unavailable if it is seen and the player does not have line of sight to it.

After deciding the scope of the player:
	repeat with X running through unavailable things:
		place X in scope.

[Uses before rules to intervene ahead of visibility checks]
Before doing something when the noun is unavailable:
	say "[The noun] [are] nowhere to be seen." instead.

Before doing something when the second noun is unavailable:
	say "[The second noun] [are] nowhere to be seen." instead.

test me with "x red ball / x blue ball / e / x red ball  / x blue ball / w / put red ball in box / x red ball / close box / get red ball / open box / get ball / e / put red ball in box".

which yields:

Place
You can see a red ball and a box (empty) here.

>test me
(Testing.)

>[1] x red ball
You see nothing special about the red ball.

>[2] x blue ball
You can't see any such thing.

>[3] e

Other Place
You can see a blue ball here.

>[4] x red ball
The red ball is nowhere to be seen.

>[5] x blue ball
You see nothing special about the blue ball.

>[6] w

Place
You can see a red ball and a box (empty) here.

>[7] put red ball in box
(first taking the red ball)
You put the red ball into the box.

>[8] x red ball
You see nothing special about the red ball.

>[9] close box
You close the box.

>[10] get red ball
The red ball is nowhere to be seen.

>[11] open box
You open the box, revealing a red ball.

>[12] get ball
(the red ball)
Taken.

>[13] e

Other Place
You can see a blue ball here.

>[14] put red ball in box
The box is nowhere to be seen.