Are you asking whether you should leave the forum? If so, you do not need to leave the website. I'm not actively planning to kill myself right now, and I stick to the recovery forum. I think it's good to have a place where you can talk honestly and receive peer support. It's also good to have a distraction, talking to folks online, when you're not feeling great.
Now, if you are asking whether you should leave, as in CTB, that's a different question. You're posting in the recovery forum and saying it's just one thing you are considering; I think you should spend some time seeing what else your life can hold. Just because suicide has crossed your mind doesn't mean you should take that path. You can have those thoughts and recognize them as only thoughts, not something you need to act on.
Did the breakup cause you to consider suicide, or has breaking up decreased your thoughts of suicide?