UPDATE 2: Darkspore has returned to Steam.
There it is, available to buy, for Ł15.
UPDATE 1: EA has responded to the Darkspore crisis, by stating on the game's official fourms that it was an error that's since been fixed.
The full statement said the following follows:
"We recently resolved an issue that was causing some players to not be able to connect to the game. If you any encounter any other issues, please contact help.ea.com for customer support. We will continue to support Darkspore, so feel free to continue to discuss the game here."
ORIGINAL STORY: Persistent DRM-related errors are killing Darkspore for a portion of the community. They can't log in and play the game, there's no workaround and, worryingly, there's no hope of a fix.
Wrote Inquisitor_Laine on 2nd May 2013: "Error has gone unfixed. Likelihood of it being fixed is zero. Sorry guys & girls."
The error is numbered 73003 and seems to be a server-side problem. At the start of the year, Inquisitor_Laine wrote an update in the forum saying EA had released "resources" to refresh, repair and rectify problems with the servers. This worked temporarily before the error re-emerged.
Spicing things up is a comment related to a more recent error, numbered 3, that was apparently fixed yesterday.
Wrote EA_Offspring on the Darkspore forum: "Hey davidyun, I'm glad it's working for you. We found a problem on the back-end and fixed it Friday but someone here doesn't seem to want the information to be sent out."
The conclusion drawn by the community is that EA has abandoned Darkspore, a largely ignored - because it was mediocre - action-RPG from mid-2011.
I've made contact with EA and I'm waiting for a formal response.