Welcome to the forum.
Hopefully someone can help - not sure the issue. However, might try the basics: compression, fuel and fire.
Try a compression test cold and when it's not running. See how much it changes.
Could try spraying gas into the carb when it won't run and see if it's starving.
Is the spark good when it's hot - magneto could be shorting out when hot.
I'm writing this and just hit me - is the gas cap vent plugged? Try removing the gas cap when it won't run.
Good luck.
By the way, the specs on the Wisconsin web site indicates the AEN as 9.2HP.