In a recent blog, Apple said it had fixed "more than 70 bugs", but admitted that 10 per cent of emails might have been lost for good.
MobileMe is Apple's answer to "cloud computing", in which information is stored on a remote server and updated via any device that is connected to the cloud.
However, some customers of the new service found that they were unable to send or receive emails, and others had issues synching up their devices.
Apple says it had a serious problem with one of its mail servers which blocked some members' access to their MobileMe accounts.