If your Wordpress happens to be fronted by Varnish you might get some
mileage out of using Edge Side Includes (ESI)

    https://www.varnish-software.com/static/book/Content_Composition.html#edge-side-includes

If you google for Edge Side Includes and Wordpress you'll find some
articles like this describing how ESI's were used with Wordpress:

   http://timbroder.com/2012/12/getting-started-with-varnish-edge-side-includes-and-wordpress.html

So, it might be do-able.

//Ed

On Tue, May 28, 2013 at 5:30 PM, Wilhelmina Randtke <[log in to unmask]> wrote:
> In a Wordpress site, is there a way to allow site-wide caching, but force
> certain areas of a page to reload on each visit?
>
> For example, if  on a specific page there is a huge navigational menu that
> never changes, a map that rarely changes, and hours of operation which
> change frequently (as often as holidays), is there a way to force only the
> hours of operation to reload when a person revisits the page?
>
> -Wilhelmina Randtke