In 2 Corinthians 4:7-10 the apostle Paul laid out some pretty grim circumstances. He said that even when we are perplexed, we are not in despair; when we are afflicted, we are not totally crushed. If adverse situations like the reasons we care give (illness, traumatic brain injury, physical limitations, etc) are a sign of no faith then Paul had no faith. A further study into 2 Corinthians 11 and 12 will show that Paul went through all kinds of trouble - yet we do not consider him to be faithless.
Be encouraged today that faith isn't a magic potion to make trouble disappear; it is the substance that will carry you through today. Faith says I trust God no matter what. Faith sees adversity put pushes on anyway. I think caregivers must be people of great faith as we see the adversity and embrace it. We cannot make it go away, but we can do what we can to help. That requires faith, hope and love.