From Kyogyoshinsho, chapter 5:
If, when I attain Buddhahood, my life-span should be limited, even to the extent of a hundred thousand kotis of nayutas of kalpas, may I not attain perfect Enlightenment.
(The 13th Vow - the Vow of Immeasurable Life)
The life of the Buddha of Infinite Life is so long that it is impossible for anyone to calculate it. To give an illustration, let us suppose that all the innumerable sentient beings in the worlds of the ten quarters were reborn in human form and that every one became a shravaka or pratyekabuddha. Even if they assembled in one place, concentrated their thoughts, and exercised the power of their wisdom to the utmost to reckon the length of the Buddha's life, even after a thousand million kalpas they still would not reach its limit.
(Fulfillment of the 13th Vows - the Larger Sutra)
Since Amida attained Buddhahood, ten kalpas have passed;
His life-span is indeed beyond measure.
(T'an-luan's Hymns in Praise of Amida Buddha)
From The 48 Vows of Amida Buddha, p. 13-14: (also see here only the chapter)
This vow simply means that his transcendent manifestation(Sambhogakaya body or Dharmakaya as compassionate means) will last forever for the benefit of all beings.
Amida Buddha as an Enlightened Person with his transcendent body, will last eternally as the 13th Vow promises. Even “a hundred thousand kotis of nayutas of kalpas” is still limited timewhen measuring the life span of Amida, so thissymbolical number is mentioned again to suggest the infinite andimpossible to calculate life of this Buddha’s body.
From Honen's Commentary on the Three Sutras of Pure Land Buddhism (Promise of Amida Buddha, p. 77):
Moreover, in order to provide eternal deliverance for sentient beings through the essential vow, Amida Buddha vowed that his lifespan will be immeasurable. This is the thirteenth vow. To summarize, while the vow of immeasurable light was designed to reach all sentient beings throughout space; the vow of infinite life was designed to benefit all sentient beings throughout time.
Chinese Pure Land.
From Ouyi's commentary to the Smaller Sutra:
infinite life extends through time and reaches through past, present, and future ... Because sentient beings and Buddhas are inherently equal, those who invoke the name of Amitabha will be no different from him either in their light or in their life span. ... Given the truth of infinite life, the people in the Land of Ultimate Bliss are in the position that they are certain of attaining complete enlightenment in a single lifetime, and will not be reborn in different forms.
The life span of Amitabha Buddha is infinite, and here when the sutra just speaks of ten eons, this is just a provisional way of teaching. In fact Amitabha's time has been endless, and he has urged, is urging, and will urge all the sentient beings of the past, present, and future to quickly seek birth in the Pure Land, share in the infinite life of the Buddhas, and accomplish this all in one lifetime.