FEA models should always be solved on a local drive and never on a network drive. The reason is the very large difference in the speed of reading and writing of data. I don't know that ANSYS prevents solving on a network drive, I never tried it.

Can you save your project to the local E:Temp folder at the start of a project? 

I suggest you do all the solving on that local E: drive and only when you are finished, create a project archive .wbpz file on the E:Temp folder, then copy that .wbpz file to the network Z: drive.  When you want to do some revisions on that project, you must copy the .wbpz file back to the E:Temp file and restore the archive onto the E:Temp folder and do your editing and solving and repeat the archive process and copying the new archive back to the Z: drive when you are done.