I am a baptized believer. I try my best to be obedient. I try to pick up my cross and follow Christ daily. I fail a lot! Is it possible to have sinned so much that I won't be saved?
God isn't looking for perfect people because there are none. He is looking for people willing to strive toward perfection. "If we say that we have no sin, we are deceiving ourselves and the truth is not in us. If we confess our sins, He is faithful and righteous to forgive us our sins and to cleanse us from all unrighteousness. If we say that we have not sinned, we make Him a liar and His word is not in us" (I John 1:8-10).
There is no quantity limit. That was the point Jesus made to Peter. "Then Peter came and said to Him, "Lord, how often shall my brother sin against me and I forgive him? Up to seven times?" Jesus said to him, "I do not say to you, up to seven times, but up to seventy times seven"" (Matthew 18:21-22). Jesus isn't saying, either, that you only have 140 chances. The point is that forgiveness is offered as often as the sinner repents.
Now, this isn't a blank check to sin as often as you want. "What shall we say then? Are we to continue in sin so that grace may increase? May it never be! How shall we who died to sin still live in it?" (Romans 6:1-2). The more you sin, the less likely you are to leave sin and sincerely repent. But if you are sincerely putting in the effort, God understands and is willing to forgive. You have to have an attitude that sin is not acceptable and that when you realize that you've sinned again, you do whatever is necessary to stop it from repeating.