If the gods are reluctant to give the vardan or boon of amaratva (immortality) then why are certain personalities like Ashwasthhama and other chiranjivis immortal?
Those who are born are certain to die. Only beginningless doesn't have end for the obvious reasons.
BG 2.27 - Those who have a birth, it's certain [for them] to die, Hence you don't have to grieve about inevitable
Ashwathama, shri Hanuman & all others are born with certain attributes. Though they are Chiranjivi(long lived), they are not immortal from their physical body perspective. However should [any of] they, become indifferent to various qualities & tastes of prakruti, their subtle bodies would surely identify/unify with the Brahman, which is beginningless & hence immortal.
BG 2.15 - O foremost of men, surely all these don't distress to that person(Purusha); that wise person to whom sorrow and happhiness are the same -- is fit for immortality.