Give a call to the insurance company and ask to speak with a case manager. You'll need to put her on the phone with them briefly ) unless you are power of attorney) so she can give permission for you to talk to them. I know Medicare provides a week per calendar year, and yes, it's to prevent caregiver burnout. Because without you she's likely going to a hospital, and they want to avoid paying for that.
You can also call your area agency on aging or your state's elder affairs office. Numbers should be on Google.
Even better, you can try speaking to her doctor about your current state. He/she may write an order for a respite stay. Might help insurance recognize and cover it.