It's the dilemma that faces every person with a brand - and that means you too. Every author/illustrator is a brand unto him or her self. And the honest truth is that if you don't know how to market your personal brand, you are not going to get noticed.
The other honest truth I'm laying down here is that kids are more design savvy now than they have ever been and they are as drawn to a clever use of color or an appealing font as their parents and teachers.
So the answer is yes. Always be tweaking that website. Always be improving your presentation. Don't be afraid to change things up once in a while. Keep your personal style. Keep the vibe of your brand. But give your readers new visual stimulation. Stay current and stay interesting.
Sure, there are elements that must remain static in order to become recognizable. A brand like Nike certainly couldn't suddenly forego its famous swoop - but darlin', you aren't Nike. You are in the perfect position to be tweaking.
I routinely make changes to my website graphics - but always maintain my slightly grungy style. I use a lot of black. I keep my warm colors bright and my cool colors on the smoky side. I love fonts that are distressed or a little bit scribbly. I love big, bold sidebar buttons. But within those parameters, there is a lot of room to have a little fun.
One of the greatest tips I could give authors/illustrators who market their own work (and if you aren't marketing your own work, who the heck is marketing it?) is to learn those little tech skills that will allow you to freely change colors, add graphics, and shift things around on your online pages. If I can learn how, anyone can.
You just google.
As they say...learners are earners.
If you want to sell books, or anything else for that matter, never stop learning.
Take a good hard look at your online presence now and determine where you need to redesign.