Yes, the problem is the way you are setting them up inside accordions, with multiple shortcodes on one page.
Please read the documentation on how that all works:
https://stephensherrardplugins.com/docs/pta-volunteer-sign-up-sheets-custom-fields-documentation/
This is not javascript or ajax based, so when you click on a link, the page has to refresh, and the info for the signup you click on will be in the URL parameters, such as: ?sheet_id=19&task_id=130&date=2020-03-21
That then tells my plugin that you clicked on a signup link and to output a signup form instead of the list of tasks.
I did set it up so that you could put more than one shortcode on a page, but then when you click on something that would create the signup form, it’s going to be put in place of the first shortcode on the page (your first accordion), and the output from the rest of the shortcodes will be supressed (by setting a flag to let my plugin know the form was already output). Also, since you are reloading the page when you click on a link, all of your accordions are going to reset as well. So, that really is NOT a good way to set up your page.
If you want to leave it setup that way, then I suggest you read the documentation, and put the main shortcode (with no other parameters) on some other page, and check the setting to redirect to the “main” volunteer page for the signup form, selecting your new page with the shortcode in the dropdown page select list. That way, you can keep your accordion setup, but it will go to some other page of your choosing to create the signup form where they will actually signup (which you should NOT put in another accordion).
If you created the accordions because you don’t like the default layout, then I suggest you take a look at the very inexpensive Customizer Extension:
https://stephensherrardplugins.com/plugins/pta-volunteer-sign-up-sheets-customizer/
That plugin has been given a whole lot of new features recently, including some alternate layouts and design options, as well as custom layout templates.