Short, less than 160 character SMS being split
One possibility is that "characters" is not what you think. SMS was originally designed for single-byte languages, so in languages that use non-Latin characters, one "character" in that language counts as 2 or 4 characters in the  SMS message. The problem is particularly noticeable in Chinese. Emoji also count as multiple characters for this purpose.

If your correspondent is writing in Chinese or other non-Latin languages, or makes heavy use of emoji, they won't be able to write 160 characters.