how many of them do you have all your mail syncing versus a certain amount (example... a week's worth)
To add on to what Duvi said, If you have them all to Push, it might get a little wonky/slow, especially when you're in the Mail app and refreshing them all. The thing with push and how many emails you sync, it will refresh at a very quick rate to get your emails to you right when they are delivered. It does alot more work when you refresh it yourself manually if you do not have it on Push, or some accounts are on Push and some aren't. If you receive alot of emails and you keep alot of them, storage is taken up and there is more and more flooded on the phone (of-course you can load more, but they're always there).
It really depends on your usage of the accounts and how many emails are being received. Alot more power is being pushed with all those accounts. It all depends on usage/how it's being used and what is coming through.