How do I ensure my chipset drivers stay up to date, other than checking AMD's website periodically?
There shouldn't be any other problems about it.
You can check it once a year.
Or use a driver updater software to let you inform about new drivers updates.
Just to inform you, but not use their links: go directly to the manufacturer website.
It seems
kcsoftwares dumo free is quite precise (about updates).
Check this topic for more details (click).