Brad Warrell (CEO of Stardock) posted on the Demigod forums some surprising stats on single-player/multi-player usage in the 2009 yearly report. Demigod was meant to be a multi-player game, the single player "campaign" was limited and the AI was not very good compared to good players, but only 23% of those that purchased the game ever went online to play it.
Quote Originally Posted by Stardock 2009 Report
For Stardock, the more significant shock of Demigod has been the discovery of the low number of PC gamers who play strategy games online. Demigod’s single player experience, while decent, did not get anywhere near the care that the Internet multiplayer experience did. Despite this, only 23% of people who have purchased Demigod have ever even attempted to logon to play Internet multiplayer.

Demigod continues to sell thousands of copies weekly – enough to remain at retail during the Christmas season despite it coming out last Spring – but the number of people available to play online is typically less than 2,000 at a given time. This is in stark contrast to MMORPGs and FPS’s which tend to have very large online communities.

Our conclusion is that strategy games that we make and publish in the future will support multiplayer but will not sacrifice the single player experience to do so.
Developer Gas Powered Games has continued to update and provide support to Demigod despite its work on Supreme Commander 2. At the time of writing, two new demigods are nearly completed along with a couple of significant updates.
Having a good multiplayer is important, but it is not the end-all-be-all of a strategy game. That said, the multiplayer issues Demigod had at launch severely hurt it's potential.