It's been more than 100 days since Twitter's former CEO Dick Costolo stepped down, and the company still hasn't named a replacement. The company's share price has suffered. And Twitter investors have had enough.

In a research memo, SunTrust Humphrey Robinson analysts say today that the lengthy search for a new chief executive has made Twitter's investors impatient. "We are stunned that we have now passed over 100 days since the announcement of the former CEO’s resignation, particularly since the board had discussions with him about stepping down since Dec. 2014," the analysts write. "Feedback we hear from investors is that the process has taken too long."

Investors are now looking to the board and search committee for answers, SunTrust's analysts say. The two "key risks" of the lengthy process, they add, is "continued brain drain" and "waning advertiser confidence."

Okay, so what's the issue? The analysts believe that Twitter's board needs to accept the idea of having a CEO who is also the CEO of another company. That person, of course, would be Twitter cofounder and interim CEO Jack Dorsey, who is also the current CEO of Square. For SunTrust's analysts, Dorsey's double duty as chief exec of two companies is not an issue—they say Dorsey is seen as a leader at Twitter, has been capable of running both companies since he became interim CEO in June, and will keep some senior executives at the company. "We think Mr. Dorsey as CEO is expected and supported by shareholders at this point," they say.

The issue, however, is that Twitter's board said in June that it would only choose a CEO that could be fully committed to the company full-time, signaling that if Dorsey remains the head of Square, he would not be able to take on the chief exec role at Twitter. But with pressure mounting on the board to name a replacement soon, there may be room for them to change their minds.