Keep at it!
Sounds to me like you should just keep pushing through it... my first session in APA (about a year ago) I finished both 8 & 9 as a SL3. At the time I was getting used to being a league and would let my nerves get to me. I also drank during play.
Since then I quit drinking, which has helped me keep the focus on pool, and am an 4 in eight ball and a 5 in nine. Currently I am going through a bit of a funk, having only won one or two matches in the past 3 weeks or so.
Do you have a skilled player on your team? Someone that is a 6 or better and can coach? Might wanna have them give a few tips, which is something I think I need since I've cooled off. It seems that since my skill has improved I have been getting fewer tips during play... which I think is something that greatly helped me improve. Some things I think I have gotten away from during match play:
-staying down after the shot
-taking my time during pre-shot routine
-playing smarter, such as taking a safety over trying to make a hard shot
-settling down after missing
-focus on one ball at a time, and play the table not the opponent
Since I have been playing kind cruddy lately I think I'm gonna go to the hall earlier than normal and practice (more than normal). Also, have fun! It's easier said when your winning, but while keeping focused, don't get too uptight! Hope the advice is reasonable, I think it's what I am gonna try since I've been sliding...