It is really dependant on the type of e mail service you have.
If you have an imap account such as g mail, you can set up sub files, such as save, work, family etc and move the e amils to those files. Those files will be replicated on the g mail sever, and when you place e mails into those files, they will also go there on the g mail server as well as any other devices you are using.
If you have a pop account, all you are getting is a list of e mails that have appeared at the setvice providers e mail server. They will stay there as long as the servicer provider allows.
The mail program in the pad supports both type of accounts. Note, on the pad, in set up, you tell the pad how many messages to retain in the inbox. Once that level is reached, as new ,essages come in, they will push older messages off the pad. They may still exist on the providers server, and you may be able to find them there.
In short, get an imap type of e mail account if you need the ability to retain e mails forever.
And, if it is an important email that you want to be able to refer to offline (should you ever have the misfortune of no Internet access) you take take a print screen of it [press the Home and Sleep/Wake buttons simultaneously and it is saved to Photos.] This is only practical for the occasional item, but someful useful to bear in mind.
Hi Arielc10 (and any others who have a similar issue),
Despite this being an old post, I'm going to add my own $0.02 as i think both the above posters are giving misinformation.
I use a microsoft exchange email account on my ipad (for hotmail access), and find an option in settings -> mail, contacts, calendars -> Hotmail (email account name) -> mail days to sync. This option at the end allows me to choose to sync emails for any duration from a day, a couple of weeks, a month, or forever (no limit).
If i have selected a week (for example), any emails older than 7 days will vanish from my ipad, but will still be on the mail server.
Note that only the ipad can save emails infinitely - i don't have that luxury on my ipod touch, for example.
Perhaps gmail does it differently, but I can reassure you that there are ways of keeping your mail forever on various mail services, and not just IMAP accounts.
Also, once the email's been downloaded to your ipad, it can be read offline without needing to take a screenshot.
Hope this helps :)