Knowing when, what, how and WHY to twerk TWEAK your website and logo is a big thing.
If you have a website developer that regularly monitors your website for bugs, wonderful! BUT, it's still important that your customer service and marketing/sales team make it a regular habit to monitor the site through the lens of a customer.
Please don't forget to check desktop and mobile versions of sites on iPhones and Android!
[With your trusted branding kit by your side] Adding or deleting features from a website annually will help ensure that your site remains current. You don't need to do a complete web design, just some design and performance adjustments so that when you do a redesign it won't be SO painful (they're always a pain in the bleep sigh).
I kid you not, I have come across websites RECENTLY that STILL look like this Netscape homepage from 1998.
When and if you should modify your logo is a more complex decision. Normally, the bigger the brand, the more prone for logo streamlining every 2-4 years. The modifications are so slight that the consumer doesn't even notice it (unless they are design enthusiasts).
I'm a huge fan of the Pirelli logo. It was "tweaked" every couple of years since 1910, but in 1974 they stopped making changes. It is an iconic logo, but definitely "vintage."
Preserving/maintaining or creating a vintage image is a marketing decision.
While some brands are constantly changing their design elements to stay current, some brands prefer to engage customers that are feeling nostalgic. Also, vintage is just a few steps away from ICONIC.
Start that conversation, your branding kit should help guide your steps. Is the company cutting edge or are does it fill a nostalgic void for your customers? And, don't worry if you "get it wrong," Burger King went for a "contemporary" logo for 22 years and then switched back to their classic logo style.
Just have the conversation and know the intent behind the decision.