According to a former senior executive at the company, Mistry and Frith - whose departures come at a critical juncture for Bauer Consumer Media as it looks to establish itself in the UK market - were encouraged to delay their departure. However, Bauer Consumer Media said there was no truth in the claims.
Frith, the editor-in-chief of celebrity weekly Heat, announced his departure last week.
As revealed exclusively on www.mediaweek.co.uk, the exit of Mistry, director of Bauer Consumer Media and Bauer Performance, was also confirmed last week.
In addition, Nial Ferguson, deputy managing director of the firm's men's lifestyle division, is also leaving to join rival Future as group publisher of gadget brand T3.
One former Emap executive believes the timing of the exits is not unconnected with Bauer's £1.1bn acquisition of Emap's publishing and radio arm.
He said: "The departures are the inevitable result of people incentivised to stay at the company until after the Bauer takeover."
The source claimed that Frith and Mistry were persuaded to delay their departures. "Heat was responsible for almost a quarter of Emap's profits and for Mark to leave while the company was up for sale would have been inconceivable."
Future-bound Nial Ferguson, while not wanting to be drawn on the departures of Frith and Mistry, denies that he was incentivised to stay on.
Press buyers said it was inevitable that the sale of Emap's publishing operation to Bauer would prompt high-profile departures. Several sources predicted that Anthony Noguera, the editor-in-chief of FHM, might be next to leave the company. Bauer Consumer Media would not comment.
One press buyer said: "It does not matter what company you are in, people will look at leaving if the firm you work for is being sold."
James Carter, director at Factory Media and a former Emap employee, said: "I am surprised by some departures, but less so by others. Since the inception of Emap Advertising in 2000, there has always been a niggling irritation within the publishing and editorial teams that the structure hasn't optimised the performance of the business."