Yes, being an account manager is a stressful job. In fact, being an account manager was ranked as the second most stressful job, with 73 percent of respondents rating the role as "highly stressful."
One reason for this is that account managers work in sales and, as such, are typically held to a sales quota by day/ week/ month/ quarter, depending on the company. If you're routinely not meeting that quota, not only will you likely be stressed, you could be out of a job.
If that wasn't enough, most account managers' job performance is about finding clients and bringing in money for your company. Therefore, an account manager is usually under a lot of pressure to meet quota, convert quickly, and keep approval rankings high.
Competition for the most desirable account manager careers can be fierce. Many applicants feel the need to have advanced education (e g., a master's degree) to stand out in this competitive job market.