Is it possible with it to keep the email on the server after downloading it?
Yes. You can choose to use an IMAP connection and these settings control the local storage I believe.
There are other settings to control mirroring with the IMAP server, say when you delete a message locally, if it should be deleted from the server as well, or moved to a special folder etc.
What's the problem with it?
There are a number of ways to display the folders and messages, and it blocks HTML images by default for security, so setting it up the way I like it takes extra work and each account needs to be customised the same way.
It actually works pretty well - after I install some add-ons to show levels of reply with coloured markers, and an aussie spell checker, and import/export tools for when I want to fiddle, an attachment extractor
to make it easy for me to save attachments in my filesystem and remove them from messages when I want to, plus a 'sort manually' add-on to let me sort the accounts and folders the way I want, and a 'keyconfig' add-on that lets me choose the hotkey that I want to use for some things.
It has the same vulnerability as outlook express and WLM and others by using a database to store the local messages, and you need to keep backups in case the database becomes corrupted
but with IMAP you will have one backup on the server still.
I just have all these extra things to add, and change, before it's ready for me to use.
When using the full search feature on my system - it takes a little work too.
I always have to click to sort the results by date - plus when going back and forward from the search results window to the actual messages it is a pain, as the search results window drops out of view and needs extra keyboard/mouse to get back to it. If I look at 20 different results then it's just a little annoying.