The service rolled out at the same time as the 3G iPhone
Apple has set up an apologetic blog devoted to solving the problems of its recently launched MobileMe service.
It follows a barrage of criticism of the service, which connects Apple devices to e-mail, contacts and online storage.
In posts over the weekend, the firm admitted to fixing "over 70 bugs" but that 10% of e-mail might have been lost for good.
It said the problem affected just 1% of customers.
The MobileMe service launched two weeks ago at the same time that the firm rolled out its 3G iPhone.
It is Apple's answer to the new phenomenon of "cloud computing", in which information is stored on a remote server and updated via any device that is hooked into the cloud.
But some customers of the new service found that they were unable to send or receive e-mails. Others had issues in synching up their devices.
As criticism mounted on the blogosphere, Apple was forced to open up about teething problems with the service.
The opening post of its MobileMe blog revealed that the information updates had been ordered by Apple boss Steve Jobs.
It blamed a "serious problem" with one of its mail servers which blocked some members' access to their MobileMe accounts.
It admitted that it had fixed over 70 bugs but that 10% of messages received between July 16 and July 18 had been lost.
"In the 14 days since we launched, it's been a rocky road and we know the pain some people have been suffering," it read.
It promised to work around the clock to solve the problem.
The latest entry on Sunday said that it had restored full e-mail access to 40% of those affected and expected the remainder to be restored in "the next few days".
But a quick glance at the blogosphere suggested that the problems are not over for Apple.
Writing on 28 July on tuaw.com - an unofficial weblog devoted to Apple - blogger Lon Seidman said: "It looks like my 'cloud' has evaporated. MobileMe wiped out about two- thirds of my contacts on my iPhone earlier today, and now I have zero contacts and an empty calendar on the phone."