I am experiencing exactly the same issue as this question the only difference being I am using Inno Setup instead of Sublime Text.
I can read/write to the mapped (Z:) drive with any application (notepad, wordpad, paint, etc...), even dropping into command line I have full read/write access, but Inno Setup does not even save its .iss file without giving a "Access is denied" error. As in the linked question, this message also appears to come from Inno itself.
To be clear, I am talking about the Inno compiler editor itself not being able to even save the .iss file, I am not talking about what the generated installer is supposed to do.
Unfortunately the accepted solution does not apply to Inno Setup.
I have no clue on what prevents Inno from writing to the mapped drive. As for now the only workaround I have found is to copy/paste the whole Z tree in C, use Inno (without any problem) and then re-copy/paste the whole tree back into Z, which is.. well, rather inefficient.
I am using Windows 10 2004 x64 English International, the shared resource is a NFS export from a linux server. Inno Setup is the latest 6.1.2
UPDATE: I can confirm that Inno Setup is the only application on the PC that can't write to the shared folder. Literally everything else works without any problem.
I tried uninstall/reinstall with no luck. I also tried reverting back up to version 5.5.0, still no luck. I tried to find any log whatsoever, no luck there either. For unknown reasons Inno is denied write to the network drive.
Try to disable your antivirus. I had the exact same problem and found this solution here, which worked for me. In my case, with Avast, I just had to add an antivirus exception for the Inno Setup installation folder (C:\Program Files (x86)\Inno Setup 6). If it can help anyone having the same issue.