Question: Is it so, that Amitā[bha] Buddha (i.e. 阿弥陀佛: Āmítuófó) might not always be around?
Answer: It is not so, as all Buddhas are always ‘all around’, even if without forms, in terms of the universal Dharmakāya (法身), that pervades all space and time.
Question: Why then, is there a teaching that he will be ‘replaced’ by Guānshìyīn Bodhisattva (观世音菩萨)? (Note: Guānshìyīn and Dàshìzhì/Dédàshì [大势至/得大势] Bodhisattvas are Āmítuófó’s first and second chief disciples respectively, who are in the ‘Stage Of One Life To Replacement’ [一生补处] [of Buddhas].)
Answer: Although he will manifest ‘parinirvāṇa’ to let her/him take over, he will not really be ‘replaced’, as he can still be seen, and ‘his’ Pure Land will continue to function through the next Buddha. Manifestation of ‘parinirvāṇa’ is a skilful means, to remind us of our mortality, and to urge us to practise with more sincerity and urgency, so as to meet him in his Pure Land, to not take him for granted.
However, all Buddhas’ selfless work of guiding all beings to Buddhahood is unceasing. Even after manifesting ‘parinirvāṇa’, they will continue manifesting in immeasurable other ways to help. Thus, mindfulness of Āmítuófó’s name to reach his Pure Land will always work, as vowed by him, for delivering all beings, while it has only been 10 kalpas since accomplishment of his Pure Land. To meet him swiftly, we just need to ensure that we reach his Pure Land by the end of this very life.
Question: When and how will he be ‘replaced’, and what will happen after that?
Answer: The answer is in the following summary of the relevant section of the ‘Sūtra [Of] Guānshìyīn’s Prediction [Of Buddhahood]’《观世音菩萨授记经》, as taught by Śākyamuni Buddha (释迦牟尼佛).
Although Amitā[bha] Buddha has a lifespan of immeasurable hundreds of thousands of koṭis of kalpas (无量百千亿劫), he will manifest its ‘ending’. (Note: 1 koṭi is about 10 million. 1 kalpa is about 1.3 trillion years.)
Incalculably extensive and distant kalpas later (当来广远不可计劫), he will manifest ‘parinirvāṇa’, after which the Right Dharma (正法) will abide in his Pure Land for as long as his immeasurably long lifespan (正法住世等佛寿命), able to deliver sentient beings in the same way as when he was present (所度众生悉皆同等).
After his ‘parinirvāṇa’, all the objects of treasures in his Pure Land, such as bathing ponds, lotus flowers and rows of trees with many treasures, will still constantly expound sounds of the Dharma (一切宝物、浴池、莲花、众宝行树，常演法音). Those who are able to attain ‘Samādhi From Mindfulness Of Buddha’ (念佛三昧) with mindfulness of him will be able to constantly see him.
At dawn immediately after the Right Dharma Age ends, Guānshìyīn Bodhisattva will sit under the Bodhi tree to awaken as ‘King Of Mountain With Universal Light’s Meritorious Virtues’ Thus Come One’ (普光功德山王如來), whose Pure Land named ‘Adornment Of Many Treasures Universally Collected’ (众宝普集庄严) will only be with Bodhisattvas.
He will be attended by ‘Attainment Of Great Power Bodhisattva’ (得大势菩萨), who will, after that Buddha’s (post-‘parinirvāṇa’s) Right Dharma Age ends, awaken as ‘King Of Good-Abiding Meritorious Virtues’ Treasures Thus Come One’ (善住功德宝王如), whose Pure Land will have the same attributes.
Question: How can we further understand the nature of Āmítuófó’s manifestation of disappearance?
Answer: The answer is in the following summary of the relevant ‘Question & Answer’ in the ‘Collection [On] Peace [And] Bliss’, as taught by Great Master Dàochuò (道绰大师).
Question: [If] Thus Come Ones’ reward bodies constantly abide, why [does the] ‘Sūtra [Of] Guānyīn’s Prediction’ say [that] ‘After Āmítuófó enters “parinirvāṇa”, Guānshìyīn Bodhisattva [will] next replace [the] Buddha’s position’?
Answer: This is [his] reward body’s [i.e. Saṃbhogakāya: 报身] manifesting [the] ‘form’ [of] disappearance, not [actual] ‘parinirvāṇa’, [which is only manifested by manifestation bodies (i.e. Nirmānakayas: 应化身)].
That sūtra [also] says, ‘After Āmítuófó enters “parinirvāṇa”, moreover, sentient beings [with] profound good roots, [can] still see [him] as before.’ [This] is proof [of] that.
Also, [the] ‘Treasure Nature Treatise’ says, ‘Reward bodies have five kinds [of] forms –  [forms for] speaking [the] Dharma, and  [forms] able [to be] seen,  [forms for] many activities without resting, and  [forms for] ‘resting’ [with] ‘disappearance’, [and]  [forms of] manifestation [of] no true body [or substance].’ [This] is proof [of] that [too].
How The Buddha Is Gone, Yet Not Gone For Good