Have they really been that busy for the past several months? If that really is the case, good for them! But given the trend in the agency business, things tend to slow down a bit in the summer months.
I know I sound like a broken record, but doing your own internal work is just as important as doing client-specific work. While this internal work is not billable time, it can lead to future billable work, which ensures the ongoing success of your agency.
Now is an agency’s website the end-all be-all when it comes to attracting new business? Of course not. But it is low-hanging fruit, and you’re missing a piece of the puzzle by not taking advantage of it.