Is partaking of the Holy Eucharist the key to incorruptibility of the saints? The Incorruptibles by Joan Caroll Cruz has many stories about incorruptible saints. 

These saints with incorruptible bodies are Catholic, and I never heard any Protestant, other non-Catholic Christians, or even other religions claim they have members whose bodies are incorrupt. Does the Catholic Church have a good explanation on why this is?

Does the Holy Eucharist have something to do with the incorruptibility?
Inedia, according to the Catholic theologian Antonio Royo Marín, O.P. (Teología de la Perfección Cristiana p. 845), is the &quot;ayuno absoluto durante un tiempo muy superior al que resisten las fuerzas naturales&quot; [&quot;absolute fast lasting much longer than natural forces can endure&quot;], in which only Holy Communion is received. He continues (ibid. p. 846):

Supuesta, finalmente, la sobrenaturalidad del fenómeno, habrá que explicarlo, desde el punto de vista teológico, por una especie de incorruptibilidad anticipada de los cuerpos gloriosos, que suspende la ley del incesante desgaste de los órganos y dispensa, por lo mismo, de la ley correlativa de la refección alimenticia.
[Assuming the supernaturality of the phenomenon, it will have to be explained from the theological viewpoint, by a type of anticipated incorruptibility of the glorified bodies, which suspends the law of the incessant degradation of the organs and, therefore, dispenses from the correlative law of needing refreshment from food.]

One effect of Holy Communion is attaining glory and everlasting life: &quot;If any man eat of this bread, he shall live for ever&quot; (Jn. 6:52). One can only receive Holy Communion worthily within the Catholic Church (cf. St. Thomas on whether one can receive Communion from schismatic or heretical priests). Thus, it makes sense that the incorruptibles are Catholic.
A few examples of incorruptibles who experienced inedia (cf. Teología de la Perfección Cristiana p. 845):

St. Catherine of Siena (1347–1380), for ~8 years
Teresa Neumann (1898-1962), from 1926-1962.

For more examples of incorruptibles who also experienced inedia, see The Incorruptibles.