Cassius, I agree with most of DeWitt's thinking regarding the gods not being inherently immortal -- although they do maintain immortality (ἡ ἀθανασία) in practice.
Philódēmos, On Piety, 1.40.1138:
For the devout man preserves the immortality and the supreme blessedness of god (along with all those things connected to us) – but impious towards god is he who banishes either one. The man who deliberates without anger and without weakening of favor on [god's] preparations that [originate] from himself for both benefits and harms – this shows god to be in need of nothing from humans…
[Obbink] For pious is the person who preserves the immortality and consummate blessedness of God (together with all the things included by us) – but impious is the person who banishes either [blessedness or immortality] where God is concerned. And the person who sees also that the good and ill (sent us by God) come without any unhealthy anger or benevolence – declares that God has no need of human things..
[ Ὅσιος ] γὰρ ὁ τὴν ἀθαν[ασίαν] κα[ὶ τ]ὴν ἄκραν μακα[ριότητ]α τοῦ θ[ε]οῦ σῴ[ζων (σὺ]ν ἅπασι[ν] τ[οῖς συναπτομένοις ἡμῖν) – α]σεβὴς δὲ περ[ὶ θεό]ν ὃς ἑκά[τε]ρον [ἐξορ]ίζει μὲν. ὁ δ' [ἐπινο]ῶν χωρὶς ὀργῆ[ς καὶ] χάριτος ἀσθενούσης τὰς ἐξ αὐτοῦ παρασκε[υὰς] τῶν ἀ[γα]θῶν κα[ὶ] τῶν κακ]ῶν – ἀπο[φαί]νετ' [αὐτὸν τ]ῶν ἀνθρω[πείω]ν μηδ[ε]νὸ[ς προς]δεῖσθαι...