“A month of Sundays” — it’s an expression used to convey a longsome period of time. The length of time suggested by the phrase is usually relative to how often the speaker is partial to engaging in the referenced activity (e.g. “I haven’t been to the pool hall in a month of Sundays!”), or how often the speaker believes an event ought to come ’round (“We won’t see another frog-floater like this for at least a month of Sundays.”).
The mathematical implication is that the speaker means “thirty weeks” or seven months — or thereabouts. If you’re nit-pickin’, it means 217 days for those who think of a month as thirty-one days. However, most folks lean to the thirty-day month even though there are six 31-day months on the calendar and only five 30-day months (and, of course, there is 28-day February — except for Leap Years).
But why muddy the waters with details, eh?
Why, indeed. Why not be more specific in stating a period of time? The answer is as clear as the nose on your face, wouldn’t you allow? The “month of Sundays” allusion is invoked when a person has no foggy notion of how long it’s been since he set foot in the much-missed pool hall or waded through a frog-floater in his front yard.
Still, it’s a useful way of connoting an impressive stretch of time without having to nail down an exact date and then cipher in the noggin exactly how many times the sun has crossed the sky since then. And way more elegant than saying “a long time”.