Recaptcha in a modal not working

We use 3 recaptchas on a page, one of which is on a form that only shows in a modal window. The other 2 recaptchas work fine but the one in the modal window will spin indefinitely.

I know this means that the recaptcha needs to be reloaded, but what’s the easiest way to go about doing this considering we have multiple recaptchas on the page, all using Contact Form 7’s shortcodes?