First, could you try using the editor, that is remove the .Name() and provide the model field
@(Html.Kendo().MultiSelectFor(model => model.permissionsDropDown)
Then, can you confirm there is a class for the multiselect field and that this class is used in the grid model?
I am attaching below a small sample that I made for you which seems to work fine for me, so you can run and compare against it. I deliberately chose a different name for the field for the multiselect so you can see where it goes more clearly.
You can find a more detailed example in the following repo: https://github.com/telerik/ui-for-aspnet-mvc-examples/tree/master/grid/multiselect-in-grid.
Get quickly onboarded and successful
with your Telerik and/or Kendo UI products with the Virtual Classroom free technical training, available to all active customers. Learn More.