Acutally Loui, I did the following that seems to solve my problem:
I am using Outlook (but if you are using a different mail application, I guess that a similar procedeure also will do...), so I opened Tools/E-mail account setting/Change account (then press Next)/Then I marked the account that I want to change and pressed Change/Then More adjustments/Choosed the 4th flip Advanced and then pressed Delivery and then did the following magic trick:
----> Choose "Leave a copy on the server"
This worked for me (bud I have only 20 minutes experience...)! Only problem that I can see, is that the company that own the account before or later will delete my mails because I have reach the mailsize limit...
A spin off problem to this solution is that when I send a mail from my iPad to my iPad, i receive only the mail - as expected. But when I send from my PC, I do allways receive an attachment (winmail.dat of 2,8kB). But i can not open this file, so I do not know what it is.
I have now send 5 test mails to my self, and all looks fine (if you ignore the unwanted attachment...). I then did the oposite to what i wrote above (i.e. removed the checking in "Leave a copy on the server", and then refreshed my iPad.
And guess what: All 5 mails disappeared! Dangerous...
So I obviously went back and ticked the box "Leave a copy on the server"
I do not know if I am into something here, but I would love to get a comment from one iPad-specialist to take a closer look on this subject - or at least tell me if I am doing something wrong.