If your iphone 6 email wont update there a couple different things and reasons this is happening. Bugs like this mainly happen whenever apple does some kind of update. First thing you want to do is go into your email settings and click the option fetch new data. If your iphone 6 is set to push that’s a good thing because it means your iphone constantly on the lookout for any incoming emails. This however can also be a bad thing. Instead of using the push feature turn this option off and below under fetch set your iphone 6 to 15 minutes. After you do this Id recommend restarting your iphone 6 and waiting 15 minutes to see if any incoming emails bounce in. You can also try resetting the network settings in general if this does not work. If your iphone 6 email still won’t update a last thing to consider is to delete your email and re add it which will sometimes work as well.