Do the elders keep secrets from the church?

Answer:

"Moreover if your brother sins against you, go and tell him his fault between you and him alone. If he hears you, you have gained your brother. But if he will not hear, take with you one or two more, that 'by the mouth of two or three witnesses every word may be established.' And if he refuses to hear them, tell it to the church. But if he refuses even to hear the church, let him be to you like a heathen and a tax collector" (Matthew 18:15-17).

You are reading Matthew 18:15-17 backward. The point of the passage is to minimize who knows about sins between two brethren. More people are brought in only when the problem cannot be resolved.

However, there are some who think that bring a matter to the elders is bringing it to the church. If a church has elders, they would be good ones to ask in regards to coming as witnesses, but the elders are not the church. If a matter is resolved with the elders, then there is no reason anyone else needs to know about the matter. See "How detailed does a confession of sin have to be?"

In performing their duties, elders are going to become aware of many things about members of the congregation's lives. Their job is to see that sin is dealt with and that it doesn't spread. It is not any Christian's duty to disclose the resolved sins of others.