การใช้ภาษาอังกฤษ ที่ถือว่าถูกต้องในที่นี้ อ้างอิงตามมาตรฐานของภาษา
I think 'continual' (adjective) is often used to mean 'persistent' or 'time and time again' but not necessary without a gap in a period of time. In your examples:
We lived in continual fear of being discovered. = We persistently feared we'd be discovered. (There were times that we lived normally but most of the time we feared.)
They argue continually about money. = They argue time and time again about money.
in contrast 'They argue continuosly about money.' = 'They argue about money for a long time without a break' and/or 'they are still arguing about money'.