Thanks for this question. It is an important one and one I care about more than most. I get occasional anecdotal information about this question from hermits seeking to be professed under c 603 in various dioceses. Still, I have only received a report about one diocese that excluded a candidate because of chronic illness per se; in this case, they cited the impediment to orders 1044.1 which struck me negatively in several ways. First, the candidate was not petitioning for admission to orders or to a highly social lifestyle. This made the canon noted doubly irrelevant, nor did the diocese have a general prohibition on professing anyone with any history of mental illness. If there was some such history (the canon still uses the terms "insanity" and "psychic defect") it needed to be assessed in terms of the solitary eremitical vocation and the candidate him or herself.
Also, a diocese needs to be able to give sufficient time and attention to discerning such a vocation or simply refuse to profess anyone under c 603. In the case mentioned here, this "impediment" was only noted after the candidate was asked to write a Rule of Life and had worked hard on it. (Writing a Rule is not an easy project; moreover, it takes a significant period of time, prayer, reflection, and probably, several consultations with a mentor to complete an adequate (liveable) Rule that is deeply rooted in both c 603 and the candidate's lived experience. Dioceses must understand all of this before requesting someone even begin writing their Rule, particularly if one is planning on using something like C 1044.1 as an absolute impediment to eremitical life.) Thus, in this case, the chancery's decision and justification struck me as lazy, essentially dishonest, and disrespectful. Again, it is not a surprise to find a diocese not understanding c 603 or vocations lived under it, but applying c 1044.1 after several meetings with the candidate coupled with the prior request that s/he write a Rule of Life, offends against the canon and the candidate pursuing profession under it.
Chronic Illness and the Desert Vocation:
It is especially important that a diocese recognizes that eremitical life is a desert vocation with desert spirituality at its heart. By definition, chronic illness is itself a profound desert experience. The Gospel that eremitical life witnesses to is the Gospel of a God whose power is perfected and most perfectly revealed in weakness. (2 Cor 12:9) Thus, dioceses who have a good sense of the vocation in general, will recognize not only that each vocation must be individually discerned, but that various forms of chronic illness, far from serving as impediments to eremitical life, may be important formative influences that allow one to form an essentially eremitical heart long before one embraces eremitical life in a formal or even a conscious way. This is a really critical element of the discernment of such vocations that flies in the face of much writing about eremitical life focusing on its austerity and physical demands.While some few contemporary eremitical vocations may look like images of eremitical life drawn from past centuries and instances of solitary eremitical life, and while it remains true that this vocation is demanding and should not be watered down, it is also true that theologies of prayer, penance, the silence of solitude, and the other central elements of the canon have shifted some to allow the demands of the life to be primarily spiritual and holistic, not narrowly physical. What cannot be lost sight of is the desert character of the calling and our expanding sense of the myriad ways such a vocation is encountered and expressed.
Similarly, we cannot forget what it means to witness to the Gospel in significant and fruitful ways for the praise of God and the salvation of others. Hermits are not navel-gazing nutcases who isolate themselves from the larger world for fear of being contaminated nor because they are on an entirely individualistic quest for holiness. They are individuals committed to living ecclesial lives of wholeness in a unique relationship and dialogue with God. In the silence of solitude, they do this in Christ through the power of the Holy Spirit of love and communion. When this is lived with integrity, others will also come to know that however fragile or threatened their lives, the faithfulness of God will not allow them to return to Him void. This "for others" quality is the reason for everything the hermit lives in her hermitage; it marks every movement toward authentic holiness just as it defines the risen Christ and every member of the Communion of Saints.
For the chronically ill or disabled who are already marked as separated from the world of the differently abled and whose illness isolates them, the solitary eremitical life may be the context in which their anguish and isolation can be redeemed by the love of God. In this context, the hermit becomes a person of prayer meeting the pain of a suffering world with compassion. The poverty of spirit demanded by being chronically ill can be transformed into the inner wealth of one who knows s/he is deeply regarded by God. Many of the values associated with our consumerist world, the ways meaning and success are measured are countered by the hermit, especially the chronically ill hermit. To be a person who encounters the pain and anguish of the world with the compassion of eremitical prayer is to share in the fundamental vocation of Jesus. It is to live a penitential life oriented toward health and wholeness and builds on the suffering already built into human life. Dioceses need to be able to see the possibilities chronic illness and/or disability create for authentic eremitical life.All that considered, it remains true that not all chronic illnesses lend themselves to eremitical life. This is especially true of some forms of mental illness. More to the point, however, not every person with a chronic illness will be able to come to live and pray their illness in the way a solitary hermit must come to do. While endurance is important, one is called to do more than endure the illness; one is called to allow it to become subject and transparent to the transforming love of God so the world might be blessed by it and the life of the one who suffers from it. The bottom line in all of this, however, is that the diocesan team or personnel charged with discerning and assisting in the formation of the solitary hermit must discern on a case-by-case basis with the requirements of c 603 and the life it envisions uppermost in mind. To answer your question in your own terms, No, it is wrong to exclude someone from profession and consecration under c 603 merely on the basis of a chronic illness.