Hello,

I am sorry to hear that your ground myrtle is dying. It would be very helpful to see a picture of the problem. I did find some information on  one disease in a factsheet from Penn State. Please take a look and compare to your plants.  Feel free to ask additional questions and send pictures. 

Vinca Diseases (psu.edu)

I look forward to helping you further.

It does appear that phoma blight may be the problem. Start by removing all the dead material. 

Here is a factsheet to confirm this:

Phoma stem blight of Vinca (purduelandscapereport.org)

Phoma is a fungal disease, so no pesticide spraying is needed. I am not sure if a fungicide spray would be helpful in a bed with existing disease. I think you might start by removing all the dead material and see what happens. Do not put the dead material in your compost, as it would spread fungal disease elsewhere.  It looks like the disease thrives in cool, wet conditions. Overhead watering is not recommended. Fortunately vinca can tolerate some dry conditions. I hope your vinca can recover.

 According to the article it appears that the disease can remain in the soil for several years. When you feel comfortable replanting the vinca. The following factsheet gives some advise on dealing with the disease and attempting to replant lost areas. 

Vinca Blight and Root Rot (illinois.edu)

I hope you have good luck refurbishing your ground myrtle. It sounds like it might be an awful lot of work to do so though.