Is Vishnu likewise a mortal position ?
No. Vishnu as preserver and sustainer of this universe is not a
Narayana , Vasudeva , Hari Or Vishnu are the names used for addressing Para-Brahman (Supreme Being) Vishnu is addressed as the same supreme Lord. He is Supreme Being in Vaishnavism tradition of Hinduism.
Here In Katha-Upanishad
Vasudeva or Vishnu is being called as a
विज्ञानसारथिर्यस्तु मनः प्रग्रहवान्नर ।
तद्विष्णोः परमं पदम् ॥
vijñānasārathiryastu manaḥ pragrahavānnara |
pāramāpnoti tadviṣṇoḥ paramaṃ padam ||
He who has vijnāna, buddhi or Reason, for his charioteer and a
(disciplined) manas as the reins—he verily attains the end of the
journey, that supreme state of Vishnu.
Shankara’s Commentary: Com.—What that goal is, is now explained; but the man who has discerning intelligence for the driver, whose mind
is under control, and who is clean, i.e., the knowing man reaches the
end of the road of Samsâra, i.e., realises the Supreme; i.e., is
absolved from all the ties of Samsâra. The man of knowledge attains 1
the highest place of Vishnu, i.e., the nature of the all-pervading
Brahman, the Paramâtman known as Vâsudêva (the Self-luminous).
Here In Narayana-upanishad we can see that Lord Vishnu is eternal.
अथ नित्यो नारायण: ब्रह्म नारायण: |
शिवस्च्य नारायण: शक्र: च नारायण
atha nityo narayanah brahma narayanah
sivas ca narayanah sakras
Thus Narayana is the eternal being. Brahma, Siva, Indra, time, the directions, the subdirections, up and down, inside and outside,
are all pervaded by Narayana. Narayana is everything, past present
and future. Narayana is the eternal pure effulgent Lord, without a
second to compare. He is Visnu, the Supreme Lord says the upanisad.
- Book I -Chapter Two - We can see that Rishi Parashara calling Lord Vishnu as unchangeable , eternal , imperishable , Undecaying.
अविकाराय शुद्धाय नित्याय परमात्मने |
विष्णवे सर्वजिष्णवे ||1||
Parasara said - : Glory to the unchangeable, holy ,eternal Lord
Vishnu ,of one universal nature , the mighty over all.
आधारभूतं विश्वस्याप्यणियांसमणियसाम् |
Having glorying him who is the supporter of all things ; who is
smallest of small ;who is in all created things ; the unchanged
;imperishable ;Purushottama , who is one with true wisdom , as truly
known ,eternal and ,incorrupt
प्रणम्य जगतामीशमजमक्षरमव्ययम ||7|| Lord of creation and preservation;
the ruler of the world ; unborn ; imperishable , Undecaying.
Vishnu is the "preserver" in the Hindu trinity (Trimurti) takes yoga-nidrā at the time of Prakrutika Pralaya or devastation of the three worlds. As describes Shreemad Bhagvat Puran.
अन्तः स तस्मिन्सलिल आस्तेऽनन्तासनो हरिः ।
स्तूयमानो जनालयैः ॥33॥
antaḥ sa tasmin salila antaḥ sa tasmin salila
yoga-nidrā-nimīlākṣaḥ stūyamāno janālayaiḥ
The Supreme Lord, the Personality of Godhead, lies down in the water
on the seat of Ananta, with His eyes closed, and the inhabitants of
the Janaloka planets offer unto the Lord their glorious prayers with
Purport: In the transcendental stage all activities are always
present, and they are glorified by prayers of great sages like Bhṛgu.
Conclusion - Thus from above shlokas its clear that the Post of Lord
Vishnu as a preserver and sustainer is eternal , he himself as Para
Brahman is not Mortal and his position never changes.