That depends on what you're talking about. The US Amateur Championship is actually open to NON-APA members. This is a singles tournament based on their Master's format of playing 8 and 9 ball in a race to 7.
If you're an APA member it's $50, if not, it's $75. You do not need to continue play, you can simply play in a regional qualifier and then if you win that you move onto the US Amateur Championship in Florida.
All other tournaments held by APA (think Vegas) require you to play on a team for a predetermined amount of time, as well as there are minimum game requirements.
I just quit APA but can still be playing in one of the Regionals, just mulling it over.