Last year the same problem.
My tips got moldy, but I also got mold on the soil from covering. I watered once a month to keep the soil from drying out.
This year I left everything uncovered and everything looks fine.
Last Spring, my Zingarella had mold on the tip. I clipped it off and got shoots from just under the tip. The rootball is the nerve center. As long as that is monitored, you'll be fine.