Good question. I think you are in great company, because David, for example, said, "Why, O Lord, do you stand so far away?" in Psalm 10:1.
I think it provides a level of perspective when we understand that it doesn't say, "Ask and it will be given to you immediately". Hebrews 11:13 teaches us that some people died while still enduring, yet Hebrews 6:12 helps us understand what we are called to do, which is endure, and that, in the end, the inheritance will be sure.
Jesus' teachings on prayer are focused on 2 parables. One of them is the parable of the persistent widow that has to come back and ask again numerous times. The other is the parable of the obnoxious neighbor. They both got what they were asking for, not because of their relationship with the person, but because of their persistence. With regard to this reality of persistence, I'd recommend examining the tense of the verbs in Matthew 7:7-8.
Also, James highlights Elijah as a man of prayer, and he makes it sound so easy. Elijah prayed and no rain. He prayed again and rain, but I think that's slightly misleading. I'd look at 1 Kings 18:44.
Personally I learned this through experience. I had prayed and seen miraculous things happen, including healing, and then I had, at times prayed, and not seen things happen. One day I had a serious injury, no insurance, and I couldn't sleep because of the pain, so I decided to take prayer seriously.
Every day, I would just wait on God specifically about my injury for 10-15 minutes. I didn't get healed the first time, but I just kept going. On the 5th day I was healed. Sometimes all it takes is a little perseverance, but sometimes it takes something serious in our own lives to learn to persevere even 5 days. Hannah prayed a long time. Wow.
Please, understand me. 5 days isn't a magic number. God's promises are sure, but we don't control the timing. We entrust ourselves to Him by waiting on Him. He takes action on behalf of those that wait for Him (Isaiah 64:4), but He takes action when He's ready to.
Daniel 9 is a great example of someone waiting on God for something He promised through the prophet Jeremiah. Just because God promised it doesn't mean we shouldn't pray. It means we should press into emotional vulnerability (Psalm 62:8) in response to the promise and entrust ourselves to Him.
It's also worth noting that, on occasion, Jesus Himself had to pray twice before His goal was complete (Mark 8:24). I don't expect more of myself than Jesus, just to be honest, even though Jesus said I have that potential (John 14:12).
We're called to present our requests to God as an act of emotional submission to Him. Even if it doesn't happen right away, being emotionally vulnerable with our Father is what we're called to do. That's what David models for us in the Psalms, and that's how we become emotionally healthy, rather than...backed up.
That's what Jesus was doing when He asked the Father to remove the cup from Him. He doesn't have the right to hide secret desires from the Father and be alone, but He also submitted His heart. Being known and submitted simultaneously can be tricky for those of us that are not so naturally emotionally vulnerable like Jesus was with the Father, but it's really the name of the game, and that's what the Psalms model for us.