Did the result will be always positive?

There is always a chance of having a negative test even though you have the disease. It seems like you are still suffering from Hep B, given that your core antibody test positive. I suggest you go get treatment. What did your doctor advise you?

You should know that antibodies are produced by the body to offer protection from antigens (foreign proteins).
Hepatitis B core antibody (anti-HBc) is an antibody to the hepatitis B core antigen. The core antigen is found on virus particles but disappears early in the course of infection. This antibody is produced during and after an acute HBV infection and is usually found in chronic HBV carriers as well as those who have cleared the virus, and usually persists for life.
Hepatitis B surface antibody (anti-HBs) presence indicates previous exposure to HBV, but the virus is no longer present and the person cannot pass on the virus to others. The antibody also protects the body from future HBV infection. In addition to exposure to HBV, the antibodies can also be acquired from successful vaccination.
Hepatitis B surface antigen (HBsAg) is a protein antigen produced by HBV. This antigen is the earliest indicator of acute hepatitis B and frequently identifies infected people before symptoms appear. HBsAg disappears from the blood during the recovery period.
Having positve Hepatitis B core antibody means you have already have had HBV infection and you are done with it. You cannot get infected and sick againg with the HBV. But you could be a carrier(can infect others while you yourself are healthy). You should pursue this and consult with your doctor about it.
I dont know why you need to temperorily remove it from your blood and get a positive test.
You cannot and should not donate blood to anyone.
One of the source I have mentioned (labtestsonline) they do answer questions...you could also ask them your question.