Microsoft on Monday said it had restored e-mail service to Hotmail users after many reported that their entire accounts were deleted without warning.

“We have restored the emails to those who were effected,” Microsoft said in a Monday note on its help site.

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Users who are still experiencing problems are encouraged to log into windowslivehelp.com and post details about the problem.

“We sincerely apologize and thank you for your continued patience,” Microsoft said.

Over the weekend, Microsoft’s official support forum started showing posts from people who reported that their entire Hotmail accounts were gone. Users were able to log in, but there were no e-mails in their inbox, no sent or deleted messages, and no folders.

One user reported getting an error message upon sign-in on December 31 before seeing a “new” Hotmail account welcome message.

On Sunday, Microsoft said it had “identified the source of the issue have restored e-mail access to those who were effected” but did not elaborate. For users who did not receive mail during the down time, Microsoft said it was “in the process of rectifying that and should be finished by late [Sunday] Pacific time.”

Can an “app store” refer to any brand other than Apple? Microsoft thinks so.

Microsoft has motioned for a summary judgment to block Apple from trademarking the phrase “app store,” as it filed with the U.S. Patent and Trademark Office (USPTO) on July 17, 2008.

“An ‘app store’ is an ‘app store.’ Like ‘shoe store’ or ‘toy store,’ it is a generic term that is commonly used by companies, governments, and individuals that offer apps,” said Microsoft’s Russell Pangborn, Associate General Counsel of Trademarks. “The term ‘app store’ should continue to be available for use by all without fear of reprisal by Apple.”

In 2008, the year of Apple’s applicaton, Apple launched the “App Store” to sell mobile software to its nascent smartphone, the iPhone. As the phone’s popularity took off, so has the common, though not universal, correlation of “app store” with Apple.

However, Microsoft argues in a 23-page motion (PDF), which is posted on techflashpodcast.com, that the phrase “app store” is too generic to belong to any one company:

“Terms that combine the generic name of a product with the generic designator ‘store’ or ‘warehouse’ are generic and unregistrable for retail store services featuring the product. THE COMPUTER STORE, for example, was held generic for stores selling computers,” Microsoft wrote.

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Furthermore, the motion argues, the phrase “app store” has been widely used as a generic term by members of the trade, press, consumers, and even Apple CEO Steve Jobs, to refer to any retail store offering computer software.

“Amazon, Verizon and Vodafone have all announced that they are creating their own app stores for Android. There will be at least four app stores on Android,” Jobs reportedly said in an interview, according to Microsoft’s motion.

If Apple trademarked “App store,” it could sue anyone who dared use the phrase to describe its own, er, app store.

Google and Microsoft distinguished their own retail software stores early on with names like Android Market and Windows Marketplace for Mobile, but others are less differentiated: Blackberry has App World, Samsung calls its store Samsung Apps, and HP has the App Catalog. Microsoft notes that most of these rivals, at one point, have publicly referred to their own retail sites as an “app store.”

Microsoft’s appeal freezes the status of Apple’s trademark application to “opposition pending.”

Last October, Apple successfully trademarked the phrase, “There’s an app for that.” Facebook also convinced the USPTO to block other businesses from using the word “face” in their names.

Apple declined to comment.