Asap if esa. Do you think I will get it backdated?

I recently made a claim for sdp of esa because my daughter moved out. I made the claim in July and was told over the phone they I qualified. My daughter moved out in February so I asked if it could be backdated as I was unaware I could claim it. I did a benefit check online which said I may be able to claim . I was told to send in relevant documents as proof. Today I was told they can’t backdate as I should have informed them straight away. My argument is that nobody advises you of this. I told my local council benefits office because of rent abs council tax and thought maybe they would have told me. I have appealed the decision with the caller on the phone today. Do you think I will get it backdated