There seems to be a reoccurring figure of speech in antiquity: Having not eyes to see or ears to hear. Plutarch (46–120 AD) in his Moralia uses this phrase:

While we minded our meat and our bellies, we had neither eyes to see nor ears to hear; but now the table is taken away, we are free to discourse among ourselves and to enjoy one another;

The reader can understand what is happening here. While the food is in front of the guests, the guests would rather eat than interact with each-other. The figure of speech is not that the guests have non-functioning eyes or that the guests are unable to understand. The figure of speech is that the guests have other preferences.

The Bible also uses this phrase in several locations. The figure of speech seems to be the same or similar to Plutarch’s usage:

Deu 29:4 Yet the LORD has not given you a heart to perceive and eyes to see and ears to hear, to this very day.

It seems that the process of God explaining his purposes is the mechanism that enables people’s hearts, eyes, and ears. God is telling the people the meaning of past actions and is calling the people to turn to Him.

Isa 6:9 And He said, “Go, and tell this people: ‘Keep on hearing, but do not understand; Keep on seeing, but do not perceive.’
Isa 6:10 “Make the heart of this people dull, And their ears heavy, And shut their eyes; Lest they see with their eyes, And hear with their ears, And understand with their heart, And return and be healed.”

In this verse, God lays out the mechanism for “giving people” closed eyes and closed ears. God is telling his prophet to preach so long and hard that people begin to tune him out. The mechanism is “annoyance” and “saturation”.

Eze 12:2 “Son of man, you dwell in the midst of a rebellious house, which has eyes to see but does not see, and ears to hear but does not hear; for they are a rebellious house.

In this verse, the author is criticizing people who have eyes and ears, but have chosen not to listen. This is very much in line with Plutarch’s use of the idiom.

Act 28:26 Saying, Go unto this people, and say, Hearing ye shall hear, and shall not understand; and seeing ye shall see, and not perceive:
Act 28:27 For the heart of this people is waxed gross, and their ears are dull of hearing, and their eyes have they closed; lest they should see with their eyes, and hear with their ears, and understand with their heart, and should be converted, and I should heal them.

In this verse, the mechanism is again clear. People do not hear or see because they are saturated with preaching (“their ears are dull of hearing”). People have shielded themselves from salvation.

Rom 11:8 (According as it is written, God hath given them the spirit of slumber, eyes that they should not see, and ears that they should not hear;) unto this day.

This could be a reference to several verses. Most likely it is referencing Isaiah 6:10. The context fits it nicely. God has preached so long and hard that Israel is numb. In verse 11, Paul details one last attempt to change the people in spite of their dullness. The context is fervent attempts to convince people to change.

In short, the phrase “no eyes to see or ears to hear” most likely is a figure of speech meaning that people are sick of hearing something (or are not in the right mindset) and choose not to pay attention.