The moment when you know you’re ready to grow is when you can afford to hire someone full-time to manage your site. Agencies are great but they are best used as mercenaries for hire. You still need someone on your team who can manage content changes and generally be in charge of the website.
The conventional practice has been that small businesses simply assign someone who already has another job in the company (and often has no website management experience) to be in charge of the site. That person because of their responsibility for the website yet lack of real understanding of websites and web development usually gets in the way of the developer or agency building the site. Agencies and developers would rather do everything ourselves than to have to deal with a client’s non-expert.
But if you grow when it hurts not to, if you have a purpose for your website (and web presence in general), then you’re going to get to skip the lateral promotion of someone who doesn’t know how to manage a website and be able to hire an actual expert to run your web site and presence full-time. That will be a huge boon to your business. And if you find someone with the right web management experience, maybe even experience with developers and designers, you will strengthen your ties with agencies, designers, and developers.