Do you have an idea how I can overcome this? I’ll be travelling in South America for several weeks and I bought the iPhone to keep in touch with my children but I currently have no confidence that email communications will work.
By default most PC email programs are set to automatically delete messages on the remote mail server once they have been downloaded to the computer, so if you subsequently check for messages on your iPhone your mailbox will be empty.
It sounds as though the same thing is happening when you access mail on your iPhone, though the default setting is to not delete downloaded mail. You should check to see if this feature has been enabled by going to Settings > Mail > Accounts Advanced and under Incoming Settings make sure Delete from Server it is set to Never.
If your home PC is not going to be used for emailing from your account while you are away you can leave it as it is, otherwise you need to go into the email program’s settings (usually Tools > Accounts > Properties > Advanced in Windows email programs) and set that leave a copy of messages on server, so they will always be available on your iPhone. When you return you can download all of your mail but don’t forget to change it back otherwise your servers’ inbox will fill up and some ISPs will prevent new messages from appearing when it is full
Source: Telegraph News