Vertical tabs of form fieldsets taking a long time to load
I'm almost 100% certain this problem is related to slow-loading javascript; As Mołot mentioned in his comment on the question, you should investigate whether something is holding up the JS from loading and/or processing when the page loads, using browser tools.

There might be some other JS that's being added on the page that's blocking the vertical tabs JS from loading/running. Do you have any 3rd-party (Facebook, Google, Twitter, analytics, etc.) libraries loaded on the page? There are some good tips for getting these things to not block the rest of the page load here: Non-Blocking Loading Of 3rd Party Scripts In Drupal.

Otherwise, do you have a module enabled or some custom code that's hindering/slowing the progress of the page load on that form? This is less likely, but sometimes if a module does something that requires a lot of CPU time (like looping through an entire taxonomy tree to build a form element or do something fancy to it) either with PHP or JS, that can cause the page load to take a really long time.

Vertical tab rendering (as well as fieldset collapsibility rendering) is usually one of the last things to load when a page loads. Something is blocking the page load/render progress, and if you can figure out what that is, you'll find the source of the problem. Good luck!