I have replanted that area each spring, even replaced the soil. It grows for a while, but usually it dies by the end of the summer. When it is really dry, I do put a hose by the base of the tree and let it slow-drip to keep the tree green. Older, established monkey grass is able to go longer without water. Newer, spring-planted ground cover will need more moisture until established.
Monkey grass looks best in shade or filtered sun.
A day of hot rays tends to burn the foliage. If so, the soil will, of course, dry more quickly, compounding the problem. It could be that you can remedy the problem by just watering that spot a little more than the rest of the circular bed. I would just test the soil moisture with a finger to determine if the troublesome west side is drier than the east. Every year my irises succumb to an infection of the leaves that causes them to turn brown and die.