A website like any design, will over time become out dated. The beauty of the internet is that you do not necessarily have to start all over again and design improvements can be done gradually if needed.
Often a company will have a rebrand every few years or so and it is important that these changes are carried thorough to the website. If for example a font used on a logo has been changed, then this should also be reflected on the website to ensure brand consistence.
When making any major changes to your website, it is vital that you take a full back up of the site. If you are looking at making changes that will require the site to be offline, then see if you can keep the site running while the changes are done on an offline versions until they are ready to be uploaded causing as little down time as possible.