Perhaps the issue you are having with your Carex Morrowii Variegata is that this is a plant that is reliably hardy in United States Department of Agriculture zones 6 to 9, but with protection, a few forms can thrive down to zone 5, and Ramsey County is in Hardiness zone 4a. Also. the centers of the plant may die out and fail to produce new leaves after several years. This indicates it is time to divide the plant. Division can take place every 2 to 3 years in spring. Individual clumps are then planted singly to produce brand new plants.

This sedge is an evergreen in the deep South (USDA Zones 8-9), but is not evergreen near the northern edge of its growing range (e.g., the St. Louis area), although some foliage color may persist through mild winters. Where not evergreen, foliage should be cut to the ground and removed in late winter. Propagate by plant division in spring or seeding in the fall.  It is  best grown in moist, fertile, medium to wet soils in part shade to full shade. Soils should not be allowed to dry out. Foliage color is sharper and richer in shady conditions. Foliage may bleach to unattractive shades of yellow when these plants are grown in full sun.

Below is a link to a information sheet on Ornamental Grasses in Minnesota by the University of Minnesota Extension.  It lists the ornamental grasses that are best suited for zone 4a along with the care and maintenance of them. 
https://conservancy.umn.edu/bitstream/handle/11299/51267/6422.pdf;sequence=1

You may be interested in the video by the University of Illinois Extension on the spring clean-up technique for sedges.
https://www.youtube.com/watch?v=pns5emwxmLY

I hope this information is helpful to you.