Outdated design: if at the moment, you have not changed the design for five years or more, you definitely need to seek such service.
A decrease in the number of sales is recorded: if sales have been falling for a long enough time, it is likely that the reason for this is the incorrect operation of your site and, in general, its poor usability. In this case, it is advisable to apply the redesign in conjunction with other methods, such as SEO-promotion.
Level lower than competitors: constant analysis of competitors is a very useful thing. If you notice that the competitors have become more modern and stylish, then it is definitely time to follow their example and, of course, bypass them.
If you are going to change the name, logo or update your corporate identity: in this case, this is the most natural and logical decision.
Expanding the company: when a business card-site is not enough for you, but you need, for example, an online store.