I think all of us have had this experience at one time or another. I personally went through this experience for about 2 years straight! I was so miserable. I gave up prayer and Bible study almost altogether. Still attended church and read Christian books, but didn't pray or study God's Book.
The way you put it, as "groping after him", kind of makes Him out to be a sadistic, selfish God who loves to see us squirm before him. (Just my own opinion) When a baby starts to walk, the parents want to see him succeed. They don't like to see him struggling to balance himself, always falling flat on his face. But if they always held him up to walk, he'd never learn to do it on his own. Although he falls, the constant flexing and use of his muscles strengthens them, thus eventually making him strong enough to walk on his own. So in the same way, God doesn't like to see us struggle and battle with our "walk" with Him. He hates seeing the doubt and pain that we go through, but He knows that it's ultimately for our own good.
Therefore, God often delays the answers to our prayers, because He wants us to examine the real motives in our hearts of why we're praying. Now will we ever be able to "walk" on our own without Him? Of course not. However, as you said, He wants us to move to a higher place in him (a.k.a sanctification). It is more difficult for a parent with a very short child to walk with him/her. But when the child grows, it eventually becomes easier to walk with him/her. So in the same way, God wants us to grow in Him, and we will know Him better, and know ourselves better, and to walk with Him will make much more sense to us than it did in the beginning.
So what was it that ended my long two years of misery? It was because I had received the gift, the "robe", of Christ's righteousness through believing in His atonement on the cross, but, I
never opened it and put it on!! God saw that it was time that I open the gift, that I lay down my own filthy rags of self-righteousness, and "put on the Lord Jesus Christ" as Paul said in [Romans 13:14]. I had believed that Jesus had justified me through His death, but I didn't believe that He sanctified me also through His life. Following Jesus isn't only about believing that He took the penalty for our sins so that we could have eternal life with Him in heaven. It's also about here and now, being crucified with Him and living his life through faith.
When I finally realized this, God released from the heavenly storehouse a whole new flood of knowledge and revelations of Him and His character. I have been writing so much of this new knowledge of Him down, that I seems like I can never stop writing, it's incredible!!
So I know it's a miserable feeling when it seems like your prayers hit the ceiling and drop back on your head. But remember, God never allows this to happen with the best intentions for us in mind. [Psalm 84:11] says, "...no good thing will He withhold from those who walk uprightly."
I encourage you to press on toward the mark, and don't give up!