"In the same way the Spirit also helps our weakness; for we do not know how to pray as we should" (Rom. 8:26). "But Jesus answered, "You do not know what you are asking." (Matt. 20:22). "Concerning this I implored the Lord three times that it might leave me. And He has said to me, "My grace is sufficient for you . . ." (2 Cor. 12:8-9a).
Not every petition a lawyer files in court is effectual before the judge. Having a motion denied isn’t the same as having your case thrown out -- and Christians have many "motions" denied when they pray. Consider why denied prayers have value:
First, ineffectual prayers are not unacceptable prayers. The former have a place before God as sacred incense albeit unanswered (Rev. 5:8), the latter are prayed by the lost and never reach the ears of God at all. While a non-Christian can't pray an ineffectual prayer, let alone an effectual one, the Christian can't pray an unacceptable one. God always hears and accepts His people's prayers. Only saints have "bar roll numbers" in order to make "motions."
Ineffectual prayers are not insignificant prayers. It’s easy to think since my prayer wasn't answered in the way it was prayed, then my prayer must be wrong or sinful. Rarely are any of our prayers a single seamless garment, but rather a "quilt" of wrestling with God, asking with a weak faith, groaning through despair, all "stitched" together by the Holy Spirit (Rom. 8:26-27), interceded and worn by Christ (Heb. 7:25). No cry is too small to be heard, or too weak to be ignored. God wastes no scrapes of "material" in sewing together our prayers.
Lastly, ineffectual prayers are not unprofitable prayers. Ineffectual prayers are used by God to teach us how to pray more effectual ones -- not discourage us from praying altogether. As we persevere through the silence we learn to think more biblically, focus more passionately, ask more faithfully. It’s normal to want a thorn in the flesh removed, but it's more profitable to have pride in the flesh restrained.
If the joy of the Lord is our strength (Neh. 8:10), and having our prayers answered increases our joy (Jn. 16:24), then ineffectual prayers are no small matter. God will see to it that we are on the same page with Him when we communicate. How long that "lesson" takes is up to Him, but the outcome will always be more than effectual.