There is some reality subtext here. Some years ago, when I was a juvenile, I stayed in a pediatric psychward (long story as to why) and Mother dubbed it a "retreat", which was fitting as the second time I stayed in one was so nice.
In this instance, Satsuki does stay in a mental hospital after her suicide attempt (alluded to as "that day") but she words it differently to protect her sister (Ryuuko doesn't know a lot about mental hospitals but thinks they're scary). Calling a stay in a psychiatric ward a "retreat" sounds less scary, no?
On another note, my apologies if I'm inaccurate about some things, as I don't know how mental hospitals in Japan work but, for the sake of this poem, I'm going with that some of them might look like the one Satsuki went to. Why would there be an enclosed balcony? Well, for obvious reasons, of course.
