You know I'm really not sure why they even still call it a sponsorship letter, because it's quite unusual for companies to sponsor employees for their mbas anymore.
What this is really all about is that your employer needs to say okay cool she can spend 3 to 4 days a month all the office to attend classes.
I highly recommend that you not quit the job, I would first try to demonstrate how they will benefit from this additional education. It's really uncommon and a little difficult to apply for an Executive MBA when you are no longer an executive. Or no longer employed really. Part of the goal here is to apply what you learned in the classroom back at your job.
That being said, if they are dead set against it and you want this education, then switch employers and ensure that they will give you the support you need in terms of the time off. Naturally the financial sponsorship would be nice to have, but it's really more the exception than the rule anymore.
Farrell Dyan Hehn, MBA
Admissions Consultant & Verbal Strategist MBAPrepCoach.com