I haven't used parallels or fusion in a long time, but those environments are full Windows machines. If you can't save, it's a Windows file or permissions problem.
Is your game installed on a Mac volume or a Windows volume? Try moving it to Windows if it's on a Mac volume.
Do you have writes to c:\Program Files locked out? If so, allow writes there. The save folder is in c:\Program Files\Man of the house v0.7.4c (extra)\save by default (for version 7.4c).
If neither of these work, try running in a wrapper. Instructions
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