Dear Sammy, Thanks so much for your question about whether your 'lack of relationship with God' could be holding your recovery back. This is a really important question since it is a feeling that is very common amongst Christians who have mental health issues. Let's break it down a bit together.
The first thing to point out is that you included in your question that 'you have always been a Christian but struggle to 'feel' God in your life.' For me this is a key clue to answering your question, since what you are actually asking is, 'is the quality of my relationship with God holding my recovery back.'
From a psychological perspective, you should know that some mental illnesses directly impeded the way in which we traditionally sense the presence of God. It is extremely common for example that people suffering with depression will feel that God has abandoned them since they no longer carry the sensory awareness to his presence. This is because depression and anxiety directly impact the Hippocampus; the part of the brain responsibility for feelings of connection.
Imagine that the Hippocampus is like the tuner on an old radio that is out of alignment. The silence of the radio could mean one of two things 1) Radio stations have stopped broadcasting 2) This radios ability to receive signals is faulty.
I know that you will immediately choose No.2 because that is the rational choice to make but it is a bit more complicated than that. Depression/anxiety also propagate feelings of guilt and responsibility that have little or no foundation in reality. If you become mentally unwell, not only do you suffer the emotional pain but you also relive every mistake and regret that you have ever carried.
For Christian's, this is an unrivaled torment, since we love God and through Christ have known forgiveness and a relationship with him. More that than Christians tend to couple together the silence of God with the guilt and regret that they feel and so rather than choosing No.2 they choose No.1 and believe that God has stopped broadcasting to them altogether. They question whether their current illness is in fact some sort of spiritual affliction or even a direct punishment for things that they feel renewed guilt over.
You asked if your 'Lack of relationship' with God was the problem, when in fact I would refute the idea that you lack a relationship with God. God promises in Deuteronomy 31:6 "Never will I leave you nor forsake you." What Christians often struggle with in times of depression or anxiety is his apparent silence. One of the most powerful declarations of faith was written on a concentration camp cell wall during the Holocaust it said, "I believe in the sun even when it is not shining, I believe in love even when I cannot feel it, I believe in God even when He is silent."
During times of mental illness, I believe that it is essential that we hold fast to the truth of God's love and presence for us, despite his apparent silence and not assume that he has withdrawn. I know from personal experience how hard this can be, but I also know that when the sun finally rises from behind the clouds, I had never left me in the first place.
If all of this is true, that it must also be true that the quality of your current connection with God is not a reason for your lack of progress in recovery, but is in fact a symptom of your ongoing ill-health. Perhaps, rather than assuming God's displeasure over you, you might rest in the fact that you are eternally loved and forgiven by him. If anything is going to settle your spiritual anxiety and help you focus on your recovery, it is this truth (and it is true).
I hope that this gives you some peace,