My thought on this is simple. If you REALLY enjoy riding I would not get rid of the bike unless you have absolutely NO alternative. I have been through some really tough times and I so far have not had to let go of anything that I really loved to do.
The reason being once its gone you do not have something you love to do that WILL help you get through the rough spots in your life.
Your bike is a form of mental therapy, take it away and its one more thing to become despondent over.
No don't let it go you still need a distraction to help you get through it.