Im using Yahoo! right now on my PS Vita. I don't think it gives you the Yahoo! button at the beginning to register your email, your supposed to click Other in that section, then type in your Yahoo! email.
Not sure but I know with some Android phones they sometimes require you to make a setting within your actual email itself before using it with mobile devices.
I forgot what it was called but you need to allow your email to do something so it can work with mobile devices and the mobile device can fetch your mail.
I can't say this is certain why you are dealing with the problem but maybe just maybe your email itself is not set properly to work with mobile devices. Now keep in mind some email apps on some mobiles don't ask you to set them before hand but some do, so maybe the Vita needs that option set for Yahoo before it is able to work with it.
For instance my GS3 connects to my gmail instantly just by singing in, but I had bought these smart phones for my brother and sister but they are different, they asked me to go into gmail first and set something within the emails settings before it would work with those phones. So once we signed into their emails and set this option (forgot what it was) they worked on their phones.
I haven't used email on the Vita really no need for me to but maybe your Yahoo needs something set first before it works with the Vita. Just an idea.