Thanks for your question. My name is XXXXX XXXXX I'd like to help you out.
I'm sorry to hear about what you're going through in your relationship, and I can certainly understand why you would be concerned about this being a sign that you may break up. In general a lot usually depends on the reason that he feels like he needs space. If he is just overwhelmed because of the extra working hours and assisting his parent, it's possible that the space is more about him just taking care of these things in his life right now, rather than it being reflective of a problem in your relationship.
Even if you do get the impression that there are some issues in your relationship that has caused this, there are many situations where a couple takes some space, resolves these issues, and ends up stronger in the long run for it. From what you described I would say that unless this is a direct result of a situation or problem that you've been having in your relationship, then it's certainly possible that this really is more about him being overwhelmed and needing space to deal with that, rather than him trying to end your relationship.
If this continues to go on indefinitely, then at some point you do have a right to know what's going on. As of now it seems like you've been handling this appropriately in trying to be respectful of what he is asking for, and the hope is that he will appreciate that when he is in a better frame of mind to work on your relationship. I definitely wish you the best with all of this, and if there's anything else I can do to help please let me know.