Research In Motion says it's got most non-North American users back online in Europe, although many are still having trouble with web access.
Users in the US and Canada, though, are still suffering.
"In Europe, Middle East, India and Africa, we are seeing a significant increase in service levels. Service levels are also progressing well in the US, Canada and Latin America and we are seeing increased traffic throughput on most services, although there are still some delays and services levels may still vary amongst customers," says the company in its latest update for customers.
"Our global teams are continuing to work as quickly as possible to restore full and consistent service across all regions."
One thing that really won't help is the fact that a fraudulent chain message has been circulating for the last day or two, calling on users of BlackBerry Messenger to forward it to all their contacts.
The wording of the message isn't terribly convincing.
"This message is to inform all of our users, that our servers have recently been really full, so we are asking for your help to fix this problem," it reads.
"We need our active users to re-send this message to everyone on your contact list in order to confirm our active users that use BlackBerry Messenger, if you do not send this message to all your BlackBerry Messenger contacts then your account will remain inactive with the consequence of losing all your contacts."
RIM's aware of the message, and tells users to ignore it.
The three-day BlackBerry outage has been caused by a server failure at the company's UK headquarters in Slough, following an attempt to upgrade the system's encryption hardware and software.
Unfortunately, initial attempts to fix the outage by moving to an older system only made matters worse.