That can be answered by a dictionary entry too:

https://dictionary.cambridge.org/dictionary/e...

to not take part in a physical activity such as a dance or a game, because you are tired or injured:

I'm feeling rather tired, so I think I'll sit out the next dance.

Here's another good dictionary entry. I like Cambridge, Oxford Learners, Collins and Macmillan for BE.

https://www.collinsdictionary.com/dictionary/...

If you sit something out, you wait for it to finish, without taking any action.

The only thing I can do is keep quiet and sit this one out. 

He can afford to sit out the property slump.

In the dance-example it seems to be neutral but in the example He can afford to sit out the property slump there is much involvement associated in my opinion. Obviously, the meanings are changing depending on context, right?

'To sit out' is neutral. It means 'to take no part in'. There is no inherent judgement or comment contained in the expression. (SEE DICTIONARY ENTRIES.)

That is not to say that every sentence in which it appears it will be a neutral sentence: but the clues as to the interpretation will be found in the rest of the sentence, or the wider context, or even the intonation (in speech)..

I don't think the property slump sentence is especially loaded with meaning. It can be rephrased, neutrally, as:

He has enough money that he can sit and wait for the property slump to end.

There's more meaning in the Collins sentence before it IMO:

The only thing I can do is keep quiet and sit this one out. = I'm so angry, frustrated, exasperated, annoyed, irritated, disappointed, or whatever, that I am actively choosing to keep quiet and not participate in this.

BUT: the negativity in this sentence comes from 'the only thing I can do is keep quiet' NOT 'sit this one out'

Zu "sit out" gab es gerade heute auch schon diese Anfrage related discussion: Sit out or sit out of? ...