Four days after an outage hit about 40,000 users of Google's Gmail service, most users are up and running once again, the company said Thursday. "The problem with Google Mail should be resolved," the company wrote on the Google Apps Status Dashboard early this morning. "We apologise for the inconvenience and thank you for your patience and continued support." However, the report noted that the problem, which first struck some users on Sunday, isn't fully fixed yet. "Gmail should be back to normal for the vast majority of people affected by this issue," the report on the dashboard continued. "If you are still experiencing an issue, please contact us at firstname.lastname@example.org." A spokeswoman for Google declined to give a specific number of users who are still without Gmail service. However, she did note that most of those without access to Gmail tend to be users with "very large" inboxes. And that's bad news for the heaviest users of Gmail, who just might have the most to lose from the outage, analysts said. "The people with the biggest e-mail accounts are Gmail power users," said Dan Olds, an analyst with The Gabriel Consulting Group. "They rely most on the service and probably have the most to lose if their data is gone. A days-long interruption in service is very bad for these folks." And while Google has said they're able to restore data that had been inaccessible, it's not clear if all of the e-mails will be returned to every Gmail user. "At this point, it sounds like Google can restore user data. But we don't know how current those back-ups are," Olds said. "It's possible that they don't cover the last hours or more of user activity. Days of downtime plus lost data? That's not adding insult to injury. It's adding more injury to injury." The problem started on Sunday when many users began complaining that they were missing key parts of their Gmail service, including e-mail, chat histories, contacts, folders and settings. And some reported that their accounts seemed to have been reset and appeared brand new. Google reported on Monday that the outage was caused by a bug in a storage software update. The company also said on Monday that the service would be back up and running by Monday night. That wasn't the case. Early Wednesday afternoon, Google reported that engineers were still working on the issue and service has been restored for "some users."