The points are movable sections of track, allowing trains to move from one line to another.
Network Rail engineers are on-site at Hove station, Southern said, but although they believed they have fixed the fault with the points, they need to carry out further inspections.
No services are currently running from Platform 1 at Hove, and there is a limited service from Platform 2.
Southern said train services running between Brighton and Worthing may be cancelled or delayed by up to 15 minutes.
To check your journey, visit: www.southernrailway.com