The way I see this "clients do or do not need support" is this (and this metaphor faired well with clients, to help them understand why support and maintenance is absolutely crucial): I personally don't need medical insurance either because I'm healthy most of the time. But what happens when I get sick? I need fast remedy and I want to live my life assured that there's a team of experts on standby, ready to take me in.

In my experience, it made no sense to argue with the client about maintenance when the website was "sick". All the client wanted was for us to fix it. I knew that, so I made sure I sold them a maintenance package in advance, when they "didn't need" it. A website is just like a bridge: if you build it, you're responsible for it, but it's not for free. Everything I put in the world, I am responsible for, but the client needs to pay for it.

Here's how we sold support: - 30 days guarantee period (after launch) - we were selling only annual contracts. A lot happens every month. Frameworks and libraries need updating, 404 links happen, browsers update, CMS systems get new security updates... There's a ton of things to keep an eye on as a developer, and you could create an annual plan which your client pays for monthly (give her a discount when she signs a contract).