The appointment of Zients, who was replaced Wednesday by former Microsoft executive Kurt DelBene, was seen as a sharp rebuke to federal officials within the Health and Human Services Department who had repeatedly claimed over the summer that HealthCare.gov would be working as designed for its Oct. 1 launch.
Argosh, of Sterling Healthworks, said the fact that more than 25 percent of the state-run exchanges have lost their bosses so far "says the state exchanges have varied dramatically in terms of performance at this point."
Argosh noted that several other state-run exchanges including those in California, New York and Connecticut have performed much better, with fewer technological problems, and higher rates of enrollments.
"The state exchanges that are performing the best recruited experienced heads that had private-sector experience, and even public exchange experience," Argosh said.
(Read more: Long, long, long way to go to get to 7 million: Obamacare enrollment)
He also said that states hired different companies to build their own exchanges, which led to different degrees of success.
"It's not surprising that they're going to have a range of experiences," Argosh said.
Argosh said that going forward, states that have had problems with their Obamacare exchanges should be looking to hire executives with a combination of skills that can maximize the goal of getting a large number of uninsured people to sign up via a smoothly operating online interface.
"They need a combination of management talent, marketing talent and technology talent," he said.
—By CNBC's Dan Mangan. Follow him on Twitter @_DanMangan.