The fact that God, the Glorified, heals the sickness of Christians and gives attention to them is because of His common and encompassing grace and compassion which includes all humans. He heals their sicknesses and provides food to sustain them so that they may be guided in the right path, the path of felicity, prosperity, faith, perfection and divine knowledge. God created man free and let them do things of their own free choice. He tests them by bestowing His bounties on them so that it may eventually become known as to who chooses to tread the right path and who the wrong. The righteous and the faithful are separated from others.
In addition, some Christians have no knowledgeable about Islam and they are Jahil-e-Qasir [lit. inculpable ignorant]. They are intellectually incapable and weak and it can be said that if they adhere to the human principles, they will be among people who are saved from questioning and punishment in the Hereafter.
The answer to the above question is given in two parts:
A) Inclusiveness of Divine Grace and Favor
The divine grace and favors are perfect and needless of any restrictions and limitations. God, the Exalted, is Merciful and Compassionate to all. His creational love is pervasive and for the entire creatures. God's love and bounties are due to His love of the manifestations and expressions of His attributes and qualities of perfection. All are equal to Him from this perspective and if there is any difference in the grants and favors, it is because of the deficiency of the recipient. That is to say, some human beings do not have the capacity to accept the divine love and grace in the legislative world owing to the unavailability of the conditions, potentials and requirements. For instance, those who are deviated and whose hearts are closed to the truth, do not accept guidance, faith and divine attraction.
The grace and lordship of the Lord of the universe requires Him to prepare bounties for man so that he may be able to move on towards his divine goal which he chooses of his own free will. He should benefit and seek help from material and spiritual bounties which God puts at his discretion so that he may be able to fulfill his religious duties and attain prosperity and salvation. However, some people use these bounties only to attain their world goals; they forget their duties and obligations concerning the afterworld focusing their attention only to their worldly desires and ambitions. The Holy Quran says:
If any do wish for the transitory things (of this life), We readily grant them - such things as We will, to such person as We will: in the end have We provided Hell for them: they will burn therein, disgraced and rejected. Those who do wish for the (things of) the Hereafter, and strive therefor with all due striving, and have Faith,- they are the ones whose striving is acceptable (to Allah). Of the bounties of thy Lord We bestow freely on all- These as well as those: The bounties of thy Lord are not closed (to anyone). 
Hence, God bestows His material and spiritual bounties upon most of His servants due to the fact that His compassion and blessings are pervasive extending even to the most sinful people so that they may turn to God and tread the right path. As per the verses of the Holy Quran, all human beings turn, at some stages of their lives, to God and pray to Him to solve their problems and difficulties. God helps those who turn to Him. Thus, when it comes to divine assistance and blessing in the sense mentioned above, there is no difference between [believing and non-believing] human beings; all of them are bestowed with divine bounties. However, what is important is how they act as they continue to benefit from divine bounties. In other words, are they grateful for the favors being done to them? The Quran says:
"Say: Who is it that delivers you from the dangers of the land and the sea (when) you call upon Him (openly) humiliating yourselves, and in secret: If He delivers us from this, we should certainly be of the grateful ones.
Say: Allah delivers you from them and from every distress, but again you set up others (with Him)."
Thus, fact that God, the Glorified, heals the sickness of Christians and gives attention to them is because of His common and encompassing grace and compassion which includes all humans. He heals their sicknesses and provides food to sustain them so that they may be guided in the right path, the path of felicity, prosperity, faith, perfection and divine knowledge. God created man free and let them do things of their own free choice. He tests them by bestowing His bounties on them so that it may eventually become known as to who chooses to tread the right path and who the wrong. The righteous and the faithful are separated from others.
B) Some Christians are Jahil-e-Qasir [lit. inculpable ignorant].
Although Islam is the right and easy religion and it is accepted and endorsed by the common sense and it is possible and easy to reach its reality, it is at ease with those who are not aware about the reality of Islam due to inculpable ignorance or ignorance out of incapacity. Obviously, since these people are not guilty in their ignorance, God, the Gracious, bestows his mercy and blessings upon them. If they adhere to human principles, God shall not subject them to punishment in Hell because divine punishment is for ‘Jahil-e-Muqassir’ (lit. ‘culpable ignorant’) who are obstinate non-believers. That is, Islam has reached them and they have understood its truthfulness; however, they are not prepared to accept the truth due to their obstinacy and stubbornness. [This group of non-believers deserves to be punished in Hell because despite having known the truth, they have chosen with their own free will to reject Islam. These non-believers, even though they may be of good conduct, could have attained salvation but instead have closed the path to salvation themselves as they have covered the truth and are rebellious and obstinate in relation to it. As a result, they have chosen their own predicament.] As for those to whom the message of Islam has not reached or they have been denied access to the truth or who, due to lack of knowledge, have not been able to grasp the truth, such people are ‘Jahil-e-Qasir’. Those who are termed ‘Jahil-e-Qasir’ are non-believers to whom the message of Islam has not reached, or it has been presented to them in a very incomplete and untruthful manner. If they adhere to human principles, they will be among people who are saved from questioning and punishment in the Hereafter.
For further information in this regard, refer to the following indexes:
3. Tawbah of Muslims and Non-Muslims", question 1404 (site: 1424).
 - See: Tabatabai, Sayyid Muhammad Hussein, Tafsir al-Mizan, vol.13, pg. 66 – 68, Islamic Publications Office, Qom, 5th edition, 1417 A.H.
 - Al-Isra, verses 18 – 20.
 - Al-An'am, 63 & 64.
 - A person who is not guilty of being ignorant is he to whom the truth has not reached or the truth has been presented to them in an imperfect or unreal manner in a way that it looks real to them.