The only way I can think of having a loose prop is because the locknut came lose. Which can happen if the threads had oil on it and the prop was not balanced. The vibrations may have caused the nut to come loose. The spinner is just there to look nice and to be used with starters.
The prop is held by the Locknut and the lock plate, against the spinner plate which is pressed against the drive washer. Both the driver washer and the back of the spinner plate have groves and once fitted and tightly tightened, it is nearly impossible for the prop to come loose unless the locknut comes loose. Which seems to be the case.

Clean the shaft threads and the nut with the alcohol and try again.

Got pictures?