Which word can mean to complain about something in a persistent manner?

The word that conveys the meaning of complaining in a persistent manner is "grouse." This term is often used informally to describe the act of expressing dissatisfaction or grievances, especially in a way that suggests an ongoing or habitual nature. People might "grouse" about various situations, indicating a continuous level of frustration or annoyance, which aligns directly with the notion of persistent complaining.

The other words do not capture this specific sense of ongoing complaint as effectively as "grouse." "Rail" typically refers to a more vehement or forceful expression of criticism but can imply a louder, more aggressive manner rather than a steady complaint. "Table" is related to postponing or setting aside a discussion or proposal, thus having no connection to complaining. "Quail" refers to a form of shrinking or cowering in fear rather than complaining, making it unsuitable in this context.