What about the incident at Blachernae?
According to Eastern Orthodox Sacred Tradition, the apparition of Mary the Theotokos occurred during the 10th century at the Blachernae church in Constantinople where several of her relics (her robe, veil, and part of her belt) were kept. On Sunday, October 1 at four in the morning, St. Andrew the Blessed Fool-for-Christ, who was a Slav by birth, saw the dome of the church open and the Virgin Mary enter, moving in the air above him, glowing and surrounded by angels and saints. She knelt and prayed with tears for all faithful Christians in the world. The Virgin Mary asked her son, Jesus Christ, to accept the prayers of all the people entreating him and looking for her protection. Once her prayer was completed, she walked to the altar and continued to pray. Afterwards, she spread her veil over all the people in the church as a protection.
St Andrew turned to his disciple, St. Epiphanius, who was standing near him, and asked, "Do you see, brother, the Holy Theotokos, praying for all the world?" Epiphanius answered, "Yes, Holy Father, I see it and am amazed!"
An icon of the Virgin Mary praying, surrounded by people, was said to be kept in the Blachernae church. It is said to reproduce the events as St Andrew saw them that day.
What a wonderful example, no? She asked in earnest on our behalf. She, herself, didn't manifest the miracle, but, through her intercession the people were saved.
What's to say that is the case in all miracles attributed to her?
One of the 10 Commandments teaches us to respect our Mother and Father.
When Christ turned the water into wine at the wedding in Cana, He stated that it was not yet time for Him to reveal Himself. Yet, because His mother asked this of Him, He could not say "no" to her (per the Commandment).
Using that as an example, wouldn't it be accurate to assume that if she asks Christ today to grant us whatever it is that we are asking for help with, that He would listen to her?
I'm not saying that Christ takes "orders" from anyone, however, it is harder to say "no" to One's mother.