What app are you using for email? How many accounts do you have in this app, and how many emails do you have in each account?
Not knowing what app you are using it's difficult to say what is going on, however here are some things to look at and consider;
1. If you are using the stock app consider using a 3rd party app.
They usually offer more and better features and allow multiple account setups. I can only speak for Maildroid, but Maildroid will archive emails after so many are present in an account. In this way it keeps it's memory need low and won't bog or overload the app with old items. Again with the features, Maildroid offers spam blocking and a one stop inbox for all of your accounts so that you can see them all in chronological order in one spot. Other apps may offer similar features, K9 is one that I see popup in response to threads like this one all the time.
2. Is your app storing sent emails on the device or on the server?
If you can reduce the memory draw on your device by storing emails on the server rather than the device. Your issue really sounds like a low resource issue, which could be due to too many emails, SMS and MMS items being stored on your device. Yes I know SMS and MMS are not related to email, but the memory they use can affect other apps.
3. Staying with the possibility that it's a resource issue, when is the last time you cleared a cache, deleted an SMS or MMS?
Facebook is one that is know for being a resource hog clearing the cache for FB alone has solved many issues, but do not neglect caches for other apps also, and the 1000 MMS messages we all get everyday. They all use your memory resource and sometimes they get greedy.
4. Has the app recently updated or changed in some way?
Even if it hasn't we're talking about email so there's nothing to loose by uninstalling it and putting a fresh install on your device. You may have to enter your email and password again, that's the part I hate cause I always forget mine, but a lot of times a fresh install is just what the doctor ordered. If you are using the stock app you can uninstall the updates and reinstall them giving you a similar effect.
5. Restart your device.
I mention this last because not all of us but some of us over look this small thing because we're connected 24/7. Restarting the device can solve a lot of issues especially after updating apps, or making other changes.
Anyway without more details this is a basic list of things to look at. Respond to the questions posted and more advice will come.