In Agents of S.H.I.E.L.D. GH-325 has made Coulson and Skye come back to life. Why didn't that alien himself come back to life with GH-325 inside his body? And why could he even die?
Because GH-325 wasn't inside the Kree...it was derived from the blood...which is not the same thing.
The Kree dies because even though he probably healed rapidly (as we later see) it doesn't mean he couldn't be killed. If the damage is severe enough even Kree can be killed.
Whilst Coulson was killed, the GH-325 was only one of several treatments he was subjected to restore him to health.
Skye wasn't killed although she was severely wounded and being an Inhuman already had enhanced DNA
When administered, the drug causes rapid healing by promoting advanced cellular regeneration, healing severe and fatal wounds, and in some cases can even revive the recently deceased.
That blue alien's synthesized blood became the source of healing but the alien itself had major missing limbs.
And we didn't see the fluid having powers to regenerate missing limbs. And how GH died is mystery till now so all would be speculation.
And in comics Kree need more nitrogen to breathe comfortably.