I have a bit more detail after further troubleshooting

Link to the store: https://www.chemsw.com/Software-and-Solutions/ChemSW-Store/

Shipping field updates always seem to fail when checking out with a cleared browser cache and history.  The page reloads when a shiping options is selected, but the shipping value does not update.

After other activity however, (e.g. deleting an item, adding an additional item, returning to the store then back to the cart, etc) the shipping field seems to behave exactly as expected.  The page refreshes when a selection is made and the total updates. 

Once it is working, it contiues to work just fine until I clear my cache and my cookies, at which point it again validates, but fails to update the total.

Thanks for your attention Kevin,

It looks like the link you sent me does not use custom fixed ship methods, but rather a shipping calculator.  On the site mentioned above I'm using the custom shipping methods options, and this seems to be the root of the problem.

Additionaly, I completed the form on the test site you sent, and recieved an error when clicking on calculate shipping:  "A critical error has occurred.
Input string was not in a correct format."

Craig,

Its ok for you to change the configuration of the test site to match your site.

The current version of the cart v.4.28 is being used on the test site www16.smith-consulting.com.
Version 3.98 is more than 3 versions back so we are not able to test the cart to replicate the issue you reported. To confirm the issue is fixed in the latest version of the cart you can download the trial version and then upgrade to the latest build to fix the issue.

Email me at kevin@smith-consulting for the login credentials to the test site.

Thanks, Kevin