A topic in Christian apologetics and atheism is "the problem of unanswered prayer". I put that in quotes because there are at least two (alleged) problems of unanswered prayer, and it's useful to distinguish them for clarity of analysis.
i) The existence of God
An atheist will say the reason God doesn't seem to answer prayer more often is because God never answers prayer, and that's because there is no God to answer prayer. God only seems to answer prayer sometimes is because believers confound coincidence with answered prayer. They remember the hits but forget all the misses. Answered prayer is an artifact of sample selection bias. What's left over when you ignore all the misses.
A basic problem with that explanation is that an atheist must shoulder an astronomical burden of proof to make good on his claim. The onus is on him to show that every purported answer to prayer is sheer coincidence.
As a practical matter, it's simply impossible for an atheist to directly discharge his burden of proof in this regard. He could barely scratch the surface. In the nature of the case, most purported answers to prayer go unreported. These are private incidents that happen to unknown believers. In the vast majority of cases, there is no public record to assess. An atheist must dismiss it out of hand without ever examining the evidence.
The best an atheist could attempt is to discount answered prayer indirectly by disproving God's existence. However, that's viciously circular inasmuch as instances of answered prayer would count as evidence for God's existence.
ii) The fidelity of God
The issue here is whether certain prayer promises in Scripture are true. Does God keep his promise? Can God be trusted to do what he says he will do in answer to prayer, or is there a glaring discrepancy between the scope of promise and the scope of performance?
That's something I've discussed on different occasions from different angles, so I won't repeat myself here. I'm just disambiguating the issue.
Of course, calling this the "problem" of unanswered prayer is, itself, somewhat prejudicial or question-begging. It's a conventional designation, like the "problem of evil". Whether it's truly problematic is the very issue in dispute.