The Nature of Middle-Earth has this to say:
The Eldar were "fading": whether this was by the original design of Eru, or a "punishment" for the sins of the Eldar, is not certain. But their "immortality" within the Life of the World was guaranteed, and they could depart to the Blessed Realm if they willed. (p156)
This is written authorially, not placed in the mouth of a character, and I cannot find anything more definitive. However, I think it is more likely to be by design, keeping in mind that the addition of the Children into the Theme occurred after Morgoth had caused the marring of Arda. That is, in Arda Unmarred, this would not have been Eru's design; but within Arda Marred, this is how he chose to create the Elves. And all other references to the Fading of the Elves, within the Nature of Middle-Earth and in Morgoth's Ring, seem to suggest that the hroa burns out due to the fundamental nature of its materiality within a fallen world - materiality which can only be sustained where the world is most free of Morgoth's influence, in Aman, by the Valar. This is supported by Finrod's thoughts in lfurini's excellent answer. In any case, given that these are the only two possibilities Tolkien mentioned, it seems to exclude the possibility that the Summons has anything to do with it.