I presume you are using a computer (things are similar but slightly different on a phone)? Off the top of my head, and you probably already know this but just in case, make sure you check mark the "Remember Me?" box before you log in, otherwise you will have to log in again every time you come back to the forum after having closed your browser or the AzBilliards tab.
Also, your log in info is stored in a cookie, and that stored cookie is what keeps you "logged in" even after you leave the forum. If you delete all your cookies, it automatically "logs you out" so to speak since it deletes the cookie that was storing your log in information and therefore the next time you come back you will have to manually log in again as a result.
Even if you didn't manually delete your cookies, you may have have software running such as CCleaner or something similar that is deleting your cookies on a set schedule. In your browser there is an option to white list any websites for which you never want the cookies deleted, so just place azbilliards.com and forums.azbilliards.com in that "cookies to keep" white list so that it doesn't delete those specific cookies even when you manually delete all the rest of your cookies with the browser. Similarly, CCleaner and other similar software also have a way to permanently white list/keep selected cookies even when the rest are deleted. It will be somewhere in the options of the software.
Most obvious of all, and just in case you were having a brain fart of the type that happens to us all from time to time, make sure you aren't logging out of AzBilliards when you leave. As long as you had "Remember Me?" check marked when you logged in you should not have to log in again if you last left AzBilliards by closing the browser, closing the AzBilliards tab, or even shutting down the computer, but you will have to log in again if you left AzBilliards by logging out.