Hello Ricard,
Thank you for reaching out and I am happy to help!
Can you please share if this section is on a specific page (and share the URL of the page if possible) or is it embedded in the one-page website?
In W3 Total Cache you can exclude pages from being cached in Performance>Page Cache>Advanced>” Never Cache following pages” or, you can use Page Fragment Cache to wrap the specific PHP code with and therefore exclude this part of the page from being cached.
Please check the FAQ in the link provided for more details about Page Fragment Cache.
I hope this helps!
Thanks!