Question about bleach/laundry. Please help!?

I just moved a few months ago. I was looking through a tote bin full of my clothes and I found one of my old white t-shirts. It's pretty dingy so I've been soaking it in warm bleach water. I've done this about three or four times in the past almost week and it doesn't seem to be getting any whiter. My question is this - Is there something else I can do to make it white again, since the bleach is not helping at all? Or should I just toss it and go buy a new one? It was one of my favorite shirts so I don't really want to toss it.. Any advice would be great! Thank you.