Why is reCAPTCHA image fade in/out so slow?

Wysiwyg is mostly correct. Captcha Type (I'm not a robot vs solving Captchas) and fading speed depends on Google and how your score for Human vs Bot is. Your score ranges from 0.0 (a bot) to 1.0 (definitely human). In the case Google is confident that you are human, then a click to I'm not a robot is enough. The worse the score is, the more and more and slower fading captchas you will get.

If you are using a shared IP address on a VPN, this means that you are not the only person using that IP address and that other people are using it as well.

What Google sees is a lot of searches that originate from the same computer which is something that is commonly done by bots and spammers. Because of this, Google requests that you verify that you are a human by requesting that you complete a Captcha occasionally. This will prove to Google that you are not a computer program that is making fake searches.

So it's not necessarily the fact that you're using a VPN. You just don't have full control of your score if you're using an IP that is shared. It's probably likely that bots are also using that same VPN or IP and driving down the score from time to time.