Technology changes and changes FAST.
Modern websites now have "must have" features that were not evident just a few years ago. Security challenges always exist and vulnerabilities are continually being identified and must be promptly remedied.
A well-designed website should last between 3 and 4 years, with maintenance. At that point, a major web update can be expected to be required. That would be a separately priced re-design.
An example of a major change in website design occurred when the industry moved from static HTML websites to content management sites with server-side processing.  In old HTML sites, each page was separately designed and the site itself did not perform data functions. The pages were more like paintings that just sat there until the designer altered the code behind that painting.  In content management (dynamic) sites, the pages shown to the user are OUTPUTS from PHP code. The sites are hosted on servers that have databases and the sites themselves perform functions like member management, searches, web commerce, and many other valuable functions. That is also known as "server-side processing." Clients of ours with HTML websites expressed a desire to have functions possible with newer technology, but the HTML sites could not be adopted for such uses as they were not capable of such functions. Therefore a completely new site was required in such circumstances. We have not maintained a pure HTML site in many years.
Another big shift occurred when Apple chose not to support Flash. For years animations displayed by websites were designed in an Adobe product called "Flash." Web browsers used a Flash plugin to display the animations. Flash was a proprietary standard. Apple's Steve Jobs decided that his products were not going to support Flash. So, a person using an Apple desktop or early iPhones could not see those animations. The result was the prompt abanding of Flash in favor of a new standard called HTML5. In no time, Flash-based websites become obsolete and had to be replaced. This sea change commenced in 2010.
Another big change was the need to make websites "responsive," whereby the website would alter its layout to display nicely on a varied number of devices with different screen sizes. Responsive sites very quickly became an expected standard. That required web designers to edit the themes and site CSS to make them responsive.
Mashable called 2013 the Year of Responsive Web Design. Many other sources have recommended responsive design as a cost-effective alternative to mobile applications due to its ability to house all of the code in a single website. Users and developers alike began realizing the benefits and importance of mobile-responsive designs as mobile use continued to rise. This realization of importance was confirmed when Google made their announcement that search engines were going to reward responsive websites with increased rankings. https://en.wikipedia.org/wiki/Responsive_web_design
A good non-software analogy might be the purchase of a car. A warranty may exist under which the dealer fixes things that go wrong with your car and keeps it maintained. At some point, however, you may want or need features that are not available on that car. Or, the car just becomes so outdated it makes no sense to maintain it. At that point, you need to get a new car! A software example is easy. Microsoft periodically releases new versions of Windows. It supported Windows XP for years with updates, but eventually, a rewrite in the form of Windows 7 was necessary. That version was supported with updates, until Windows 8, then Windows 10 and so on.
We maintain websites that we design under our support system. However, if after a few years our clients want features that they see on newer sites, or technological changes are such that the old site cannot be reasonably maintained (often due to security issues), then a new website is the right choice.
Solia Media cannot predict the pace of change, but we do remind our clients that such external and industry-driven progress may require more than routine updates of a website - particularly if the client wants the newer features and functions which will most certainly be made possible in the coming years. In sum, we design our websites to current standards. We will maintain them as long as the industry considers it to be feasible from a technological and security standpoint. If the current platform cannot be maintained (this is not just our decision; this is determined by industry experts), we will coordinate with our clients to determine how to ensure that the client's web presence is not unduly outdated.