Social games have been synonymous with Zynga, the company that made FarmVille a sometimes maddening fixture on Facebook walls around the world. So given Zynga’s ongoing decline—the company’s stock has plummeted 75 percent since its December IPO, employees are fleeing, and its latest game titles are floundering—it’s easy to think social games are a quickly fading fad.

But plenty of investors and game developers are still writing checks and apps, betting that the average person isn’t bored with these kinds of games. The market for social and casual games is indeed still growing, but like many Web applications, these games are moving to mobile devices—a transition that has brought new challenges.

“I don’t think they [Zynga] are a guide to the future,” says Andrew Marsh, a San Francisco-based game developer whose “indie” studio Fifth Column Games recently partnered with the rapidly expanding Japanese mobile-gaming company Gree.

While the investment bank Digi-Capital recently called the Zynga IPO the peak for “Social Games 1.0” investments, it also said investors are pouring money into games for smartphones and tablets. More than half of all game playing is on such devices, NPD Group, another research firm, recently estimated.

Yet major challenges remain for companies hoping to make their games more than make a fly-by-night hit on mobile devices. One longtime game developer, Tadhg Kelly, calls it “platform amnesia”—people get excited about the same old games presented on top of new technologies, but that wears out quickly. And mobile-game companies have struggled to gain and keep users, especially ones willing to spend money. Zynga experienced this problem firsthand when it acquired OMGpop, the company behind the hit game Draw Something, earlier this year for more than $180 million, only to see the game quickly fade in popularity.

Gree, founded in 2004, is angling to succeed by creating a platform for smartphone games and courting developers like Marsh to create the next big hits. Where Zynga has struggled because it has largely depended on being seen in Facebook news feeds, Gree has created a specialized Facebook-like social network for gaming on mobile devices. Like DeNA, another Japanese company, it has found most of its current users in Asia, but it is seeking worldwide dominance with a recent spending spree and string of acquisitions.

Zynga, too, is trying to create an independent network (see “Zynga Looks to Build a Gaming Social Network of Its Own”). If it succeeds, this could help solve one problem that plagues mobile-game developers: how to get people to discover games among millions of apps in Google’s and Apple’s stores.

On Facebook, people naturally return day after day, but users aren’t as strongly inclined to open an app, says venture capitalist Charles Hudson, a partner with SoftTech VC who previously founded a company acquired by Zynga. As it is, since social elements are a less natural feature on smartphones, mobile-game companies are being forced to pour money into acquiring new users through advertising and cross-promotion. “Most mobile games are still discovered through the app store, and that’s not sustainable,” Marsh says.

Social games themselves may also need to become more creative as they migrate to mobile devices. To keep people playing, games can’t afford to get boring, says Kelly, who calls Draw Something a novelty that had no depth. Console game companies, such as Sony and Electronic Arts, and companies like Kixeye, which target more serious gamers, are starting to experiment with more casual social games for mobile devices.

Innovation could occur as developers take advantage of features particular to phones. Already, some are using feedback from touch interfaces and adapting to shorter gaming sessions—a couple of minutes while waiting for the train to come, for example.

Graphics on mobile devices are also nearing the quality of those on game consoles, especially in the case of tablets, and developers are starting to incorporate them into even simple social games. One example is NaturalMotion’s CSR Racing, a popular 3-D drag-racing game that Apple CEO Tim Cook showed off at his company’s developer conference this year.

And while no company yet has found a lasting hit game that uses phone technologies such front-facing camera motion sensors or GPS location, Hudson says that could be coming as more startups experiment.