Earlier this week, in a shock move, it was confirmed that Simon Wright, chief executive of Shrewsbury & Telford Hospitals NHS Trust (Sath), was leaving to take a job with another NHS organisation.
Now Mr Kawczynski has written to the chairman of Sath's board, Ben Reid, to ask why they have lost their current chief executive.
Mr Wright's announcement has raised eyebrows in some quarters due to the CEO's commitment to seeing the Future Fit hospital review over the line, and the fact that he had remained in post after the trust was placed in special measures following a critical Care Quality Commission inspection last year.
In March Mr Wright had himself spoken of his commitment to the hospital trust and the Future Fit reorganisation plan, during a visit from the Health Secretary Matt Hancock.
Speaking at the time he said: "Too many chief executives have come here as a stepping stone and the moment it has got difficult they have left.
"I intend to stick it out, work every day to make sure we are improving the position and get to a point where the care is outstanding."
Future Fit and the decision to place the trust in special measures have not been the only issues facing the organisation, which is also the subject of an inquiry into baby deaths and maternity care dating back many years.
It is understood that as many as 200 people have come forward alleging instances of poor care.
It has now been confirmed that Mr Wright will be joining the Nottingham and Nottinghamshire Integrated Care system as director of clinical services strategy.
He will start the job on July 22, although Sath has not yet been able to confirm what date he will leave the trust.
The trust is still awaiting confirmation that it can proceed with the Future Fit re-organisation of its Royal Shrewsbury and Princess Royal hospitals,
The Future Fit plan, which has been championed by Mr Wright during his four years at the trust, is currently being assessed by the Health Secretary after Telford & Wrekin Council formally called on him to scrap it.
The project, which would cost £312m, would see the Royal Shrewsbury Hospital become home to the county's only A&E, as well as taking over women & children's services.
The move would see Princess Royal Hospital Telford lose its A&E and dedicated consultant led women & children's unit.
Instead the Telford hospital would focus on planned care.
Mr Kawczynski said there were questions to answer over the move at what is a crucial point for the hospitals.
He said: "I am writing to the chairman of Sath's board, Ben Reid to ask why our trust has had such a large turnover of chief executives over last 15 years.
"Also why the board has lost current a chief executive at such a critical time for Future Fit and the investment of over £320 million."
It comes as Lucy Allan, MP for Telford, has written to the Health Secretary to call on him to shelve Future Fit.
She said: "I write to express concerns about proceeding with this reconfiguration in the current circumstances,
"The departure of the chief executive of the hospital trust has now been announced. I advised you in a briefing note dated February 3, 2019, that this was a likely occurrence, following the catalogue of serious failings by the trust and apparent inability of senior leadership to grasp the seriousness of the challenges faced.
"Other members of the senior leadership team have also departed, including the medical director. In addiction the CQC has just issued another urgent warning about shortcomings.
"It is clear that now is not the time to be forcing through a complex controversial restructuring against the wishes of local people and without the trust attempting to make the case for the proposal and without a stable leadership team."