Zip file not uploading

This is most likely due to the PHP zip extension not being installed.

Verify that the server you are using has that enabled and that the zip file you are trying to upload is not corrupted.
For the latter you would basically try to unzip it locally. If that works I would definitely say that the culprit is the missing zip-ext from the PHP install since tests I've done so far with the module have worked as expected.

Only issue I've had so far is trying to upload a file larger than what the server allows me to upload.

Closing the issue as no more replies from the reporter has been posted. Feel free to reopen with details if issue persists.