A new article has appeared which discusses Jesus' indestructible life:
Kibbe, Michael. “‘You are a Priest Forever!’ Jesus’ Indestructible Life in Hebrews 7:16.” Horizons in Biblical Theology 39.2 (2017): 134–55.
"Hebrews 7:16 suggests that Jesus entered the priesthood by virtue of his “indestructible life.” But what sort of life is that? How and when did he obtain it? If it pertains to his resurrected-human life, was he therefore not a priest prior to that moment (including, in particular, during his death on the cross)? If it pertains to his divine life (thus he possesses it always), in what sense could the man Jesus have actually died? I suggest that the author has neither deity nor resurrection in view as the source of Jesus’ indestructible life; rather, the point is merely that Jesus’ perpetual existence undergirds the oath that immediately follows in 7:17. However, Hebrews as a whole requires that we envision that existence in relation to both Jesus’ deity and his resurrection, and I argue, furthermore, that the two cohere via the divine Son’s agency in his own resurrection."