That was a common problem in the dinosaur age. Starting Win2K (?) the path+file length have been increased to 32K. Unless you have very deep directory structure you should never run to this issue. About 10 years back we did a testing to see how deep we can go using 3 char folder names and we went more than 100 folders deep.
See here for
Naming Files, Paths, and Namespaces[
^]
Since you are dealing with zipped files, you issue may be with file names. Check for the file you are trying to delete. Does it have any extension? how are you trying to delete it?