I have to ask Blain. Is it ever the believer's fault? Now, I understand that it may not be our place to determine that specifically for another and that is between them and the Lord, but in general, does something not occur due to our disbelief?
If we look to scripture we have different examples of such, do we not? In Jesus' own home town, not many were healed. The disciples when attempting to cast out a demon could not because of their unbelief, as Jesus said (in Matthew 17:20). We see it time and again, where the reality is that some people don't believe and are called to do so. The result dependent upon their belief.
While I agree that we shouldn't go around blaming the sick, we cannot in good conscience deny God's word on the matter either. God calls us to believe, to have faith. Think about what Jesus said to those that were healed, "Your faith has made thee well", right? To deny the importance of self-responsibility in the equation of healing, not only would be unbiblical it would be wrong to mislead people as to its significance. We, those seeking healing, must take an honest evaluation of our belief(s) and determine if we are in fact seeking healing or are ready to move on ("because Jesus has my new body waiting for me").
People will often profess faith for healing, but given an opportunity to speak on the matter it is revealed that while their faith is sufficient for healing it is not truly what they seek and believe for. Rather it isn't something they are pursuing but have put it in the hands of God (His will), and some do not even seek it in this life (though it would be nice they say) but are looking forward to their glorified body. This is a matter of inactive faith, being comfortable, plateauing, being complacent, and the like. Notice I said some, easy now.
Not all situations are the same. God is sovereign. Someone may have the faith to walk on water, but God hasn't called them to step out of the boat. Likewise, some may have the faith to be healed, but life ever after is their destination and it is their time. God bringing them home.
We shouldn't be caught up in the blame game, and should rather encourage one another. Console the trodden down, exhort, and bring joy. Share testimonies of God's deliverance and healing. Why? For it will spark within them that pursuant faith, that attains onto the glory of God. They need something, someone, to believe in, do they not? The Lord, who sees their every tear and into the depths of their heart.