The phases of STSG healing are imbibition (drinking) where the graft is fed by absorbing plasma that comes from the recipient, inosculation (kissing) where the new tiny blood vessels of the graft start to touch new blood vessels in the recipient, and finally neovascularization where the blood vessels mature between graft and recipient.

The radiation destroys small blood vessels so irradiated tissue fibroses, has poor oxygenation and therefore has low oxygen tension in the plasma secreted and cannot go through the inosculation phase.

This is also true of full thickness thermal or chemical burns which is why you have to excise to vascularized tissue prior to grafting.