Does the fan have no problems with other operations, e.g when you run the fan, it will stay on no problem? Is it just a problem with the light?
Also, are you turning on the light with a remote or a wall switch?
If it’s a wall switch – check the switch or have an electrician do it
It kind of sounds like there is an internal problem where the light is wired, e.g where the light wiring connects to either the wiring inside of your fan or the wiring in the home.
Check that wiring guide, should help, otherwise if you don’t feel comfortable, call an electrician
If you want a free option, call the fan manufacturer and ask.