That depends on where it is and who maintains it. If you share a Web server run by a computer services entity, you may not have to worry about this. Grabbing your own site and storing its constituent files on your own drive offers one more level of safety. Moreover, it also gives you the ability to edit and experiment with your site offline, perhaps using a notebook computer or a computer at home. There are limitations to offline browsing, as well.
Web pages can and do change whenever the Web site administrator chooses.
To keep up with the dynamism of the best sites, one must go back to the site from time to time and grab new or changed pages. The frequency required varies from hourly for a news site to perhaps monthly for a site focusing on Chaucer criticism. Moreover, the Internet is huge and growing continuously. Maintaining a site that covers a popular subject area comprehensively can be difficult and expensive. Absent the resources to stay absolutely on top of changes, one may be better off relying on tools that comprehensively index Internet sites, rather than attempting to capture everything on a massive volume of text pages.