I have 2 similar rhipsalis and they periodically shed small firm pieces when I water too often. I usually stick them back in the pot to root. It could be due to overwatering or a soil mix that holds too much water. Rhipsalis are true epiphytes and do best when the potting soil is most similar to an orchid mix and not a cactus mix.
I also grow the Blue Candle Cactus. The tall growth is due to lower light conditions than it really wants. It is reaching for the light. Mine get full, all day direct sun here in South Florida. If you could post a better picture of the brown at the base, I should be able to tell you what is going on.
