Good Morning Roselyn, 

Thank you for contacting the U of M Extension Service. 

The plant still looks alive. There are several possibilities. Could it be from herbicide drift from spraying weeds in your lawn or sidewalk cracks? Is there a dog in the neighborhood who would have relieved himself on one of your plants? Could the branch have been bumped or moved and partially broken off the plant? Have you inspected the leaves up close to look for any pathogen or insect damage? 

If this does not recover, you could prune off the dead branch and it appears the rest of the plant would survive.

From viewing your photo, there is bare soil around the plant. A mulch of dead leaves or wood chips around the plants to cover the bare soil would hold the moisture and cool the roots. 

Please click on the following link about growing vincas: https://extension.umn.edu/flowers/vinca

Good Luck!