Does it give an error or anything?
I personally don't use the DoCmd.ApplyFilter command. I use
Me.Filter = ...etc.
Me.FilterOn = True
but anyway, perhaps using Chr(34) instead of single quotes for the name would be helpful (if any names have single quotes):
DoCmd.ApplyFilter , "[casestatus]<>'Closed' AND [TickleDate] IS NOT null and [Assignedto]= " & Chr(34) & Environ("UserName") & Chr(34)
Or go with the Not IsNull function:
DoCmd.ApplyFilter , "[casestatus]<>'Closed' AND NOT IsNull([TickleDate]) null and [Assignedto]= " & Chr(34) & Environ("UserName") & Chr(34)