I am not sure but you might want to try logging into your email directly, ie Google for gmail, roadrunner for roadrunner mail. They may be on those servers, or whatever you call them and not actually on the pad.
I know with roadrunner I used to get messages stating that I was almost full with one email address. I had them deleted on the Outlook mail on the PC, but my settings were such that they were not deleted from the server, or something like that. I also had to redistribute storage space between the different email addresses.
So, your emails may be directly on your server? (Not sure that is what it is called) You might try that. Also, again, I am just guessing, but did not see any replies, so offering my ideas of what to troubleshoot. Also, do you have enough space available on the device? Maybe they can't be downloaded because you don't have room? Are they in your junk or spam folder?
These are just a few things I would check. I may be way off base with my guesses, but worth a shot.
Good luck.