In the beginning of September I went and got the depo shot, and it worked out fine. Then in the middle of October though I started to bleed and I thought it was a regular lasting period. But its still going on! If I don't go back for my second shot, will the bleeding stop?

The bleeding will likely stop, but it is very individual. Irregular bleeding is a very common side effect of depo. Some women, like yourself, experience frequent bleeding, while others will, at least eventually, find that their periods stop altogether. It would be a good idea to let your doctor be aware of the bleeding and then discuss it before getting the second injection. You may be advised to continue, and just wait and see what happens with your periods, or it may be advised that an alternative form of contraception might be better for you to use.

In most cases, its not a health issue with the bleeding, but just the inconvenience that causes some women to decide on a different contraceptive.