Why Many Fail to Receive Healing

The Bible clearly gives the reasons and that healing is promised.

Demon possession/oppression can be a cause of sickness. Jesus cast out
many demons and the result was healing. See also 2 Corinthians 7:1 for
Christians needing deliverance.

Sin is how sickness came into the world so it follows that if a
believer sins and refuses all correction from God then He can chasten
with sickness. Repentance brings healing.
The healing of the sickness, not the sickness, is for the glory of God. John 9:1-3

Christians can be ill and stay ill from ignorance of the healing Jesus provided in the atonement.

Everyone gets the measure of faith from God but it is the believers
responsibility to grow and exercise that faith (Romans 10:17 and Jude
20). If that responsibility is not met healing can be elusive. God can
allow it to send that message of our responsibility if all else fails.

They can stay ill because they do not know what Bible faith is Hebrews
11, or how to put it to work James 2:18-26, Mark 11:24, 1 John 5:14-15
to receive healing. No one gets ANYTHING from God unless they exercise
Bible faith praying according to His revealed will not "if it be thy
will".

Sickness can simply be a trial to defeat the devil, glorify God, and
refine the believer's faithfulness and character (see James 1:2-4, 1
Peter 1:6-7) which is why there is often a period of time between asking
and receiving by faith and the manifestation of the healing (Mark
11:24).
Christians get sick and stay sick for abusing their bodies. Praying
over ones food is VERY important for obvious reasons. It keeps us safe
from all the "stuff" in it.
Disobedience, unforgiveness, the negative things we say about
ourselves, wanting to be sick to use it for control, sympathy, a hobby,
ect.; involvement in the occult by Christians i.e. horoscope, ouija
board, "white" witchcraft, fortunetelling, magic practices, water
witching (water divining), Eastern religion like yoga all can and do
result in getting sick and staying sick.
There is a culture or climate of unbelief that is in the churches
which hinders those who want to trust Jesus for healing by faith from
doing so and hinders the work of healing miracles by the Holy Spirit.