Are all prayers accepted?

 Some great Torah authorities have said that every prayer is accepted — among them the Chazon Ish, the Kehillas Yaakov, and others. Is there a source for their view in Chazal?I haven’t found one.In fact, Chazal seem to say the opposite — for example, “If a person sees that he prayed and was not answered…” and other such statements. Reality also seems to show otherwise, as many — perhaps even most — prayers are not answered. Especially since the destruction of the Temple, when it is said “my prayer has been sealed off.” So their words are difficult to understand — seemingly. 

Shalom UvRacha,

The correct phrasing is: Every prayer is effective.

What this means is that even if a person’s specific request is not granted—for whatever reason—the merit of the prayer is not lost. It remains and benefits the person in other ways.

For example, someone might pray for a certain sum of money they need, but Hashem determines that receiving it now isn’t what’s best for him. The prayer may not be answered in the exact way it was asked, but the merit of that prayer is kept for later to help the person in other areas—such as health, nachat, success, and so on.