What are reasons to update your website and CV frequently, when not on the job market?

I think Jeromy’s answer is very good, but that there’s a second angle worth considering as well: it’s easier and better to update your resume regularly than all at once.

Let’s say you have a job for 5 years and then think about leaving and so update your resume. Are you really going to remember everything you’ve done? The dates of the awards you’ve won, the details of the projects? It’s far easier to update it when you make the accomplishments than have to remember or look up everything.

It’s also less burdensome. If you go five years without updating a resume, updating it would take several hours at a minimum. Counting refreshing, looking things up, and fact checking it can take a day of work even! I know a lot of people who don’t update their resume because it seems like a massive hassle. And for people who go long periods of time without doing it, it is a massive hassle. Amortizing that work over longer periods of time makes it easier.

Finally, I want to challenge your idea that everyone will just look you up on arXiv. I would generally rather read your list of papers on your website. I just don’t love the arXiv interface. That said, many people have terrible academic websites. Do put effort into making your website usable and pleasant to look at. At the end of the day, people who get discouraged are far more likely to go “whatever I’ll stop” than “maybe I should try a different website to get this info from.”

Also, making a google scholar profile and listing your publications on your website in addition to having them on arXiv makes it way easier for someone to come into contact with your body of work. Just because you exclusively find things through arXiv doesn’t mean that the people reading your work do too. The more places it’s published and the more coordinated those places are the easier time people will have finding your stuff. Again, make it too hard and people will just pass you by.

Finally, think about students. Students and wannabe-students look up professors all the time. In my experience, the first place to go is a personal website, and generally the second is Google scholar. GS is particularly popular because the “sort by citation count” feature makes it easier to find the major work you’ve done for someone who doesn’t know how to tell which papers/journals are impressive. Heck, many wannabe PhD students don’t know about arXiv, or aren’t very familiar with it. Less so in math, but even then there are people who never hear about it by the time they graduate undergrad. Again, putting yourself in the most places is key.

A CV in academia is useful to you and others in many different contexts. Applying for jobs is a very small component of that. CVs are useful to you and others. Keeping an academic CV up-to-date will often make your life easier, other people's lives easier, and may also open up opportunities for you.

Here are a few ways that having an up-to-date CV is helpful:

• Communicating achievement to others: The decision of others in relation to you may be influenced by perceptions of your experience and achievements. Your CV documents this (although google scholar profiles and personal websites can also serve this purpose). There are many examples that could be given: (a) another academic is working out whether to invite you onto a paper and wants to understand your expertise, (b) potential phd students are looking for a supervisor and are trying to understand whether you've supervised before or how much and how well you are publishing, (c) your colleagues at your own university are trying to understand what you do.
• Grants: When you apply for grants, you will need to incorporate information about your track-record and achievements. Your CV can be an up-to-date source of this information. Furthermore, you might be part of a grant that others are leading. The grant will often require a lot of information about the investigators on the grant. These other people may be able to fill out relevant sections directly from your CV.
• Annual performance review: If you have an annual performance review, it is often helpful to share your current CV.
• Internal promotion: Systems for promotions and levels vary throughout the world. In Australia/NZ/UK you typically have levels A to E. If you want to move up a level, you need to document your achievements. Having an up-to-date CV can help.
• Course accreditations and related matters: In some cases, your department or university might be seeking accreditation as an educational provider in a particular area. These often require documenting number of staff, educational attainment of staff, evidence of research active status.
• Annual or other reviews of programs: In addition to performance reviews, programs, larger research groups, and departments often compile documents reviewing annual (or other timeframes) achievements (e.g., publications, grant funding, outreach, etc.). Administrative people can go to your CV to get this information. Or it may be that you open up your own CV and copy and paste a bunch of things.