Why would a type 1 diabetic at 50 die after amputation?

Complicatiions. Sorry to hear this. By the time someone with diabetes comes to the point where an amputation is necessary, there are usually other complications like kidney and vascular disease which might get worse and lead to death. Also, amputations are often preceded by terrible infections, which could overwhelm the body, particularly one that's been damaged by the complications of diabetes.
Comorbidities. Diabetic often times may have many systemic medial issues such as cardiac, renal and vascular disease which may lead to a decreased life expectancy.