Why do type 1 diabetics experience hypoglycemia?
Key to this question is that untreated, type 1 diabetics would never have hypoglycemia.  It is insulin treatment that causes the hypoglycemia.  Insulin brings sugar down and without insulin (as the case with type 1 diabetics) sugar just goes up.    Exogenous insulin will bring sugar down in anyone, diabetic or no.  Since Type 1 diabetics use insulin all the time, there is more chance for an accident (hypoglycemia).  

Also, some Type 1 diabetics might not compensate against hypoglycemia or correctly perceive that they are hypoglycemic.  Reasons for this are laid out in the following article:

From Hypoglycemia in Type 1 Diabetes


  Three major defects in this homeostatic response contribute to the
  high frequency of hypoglycemia in type 1 diabetes.


The article summarizes what those are - basically a blunting of normal reactions to hypoglycemia stemming from the disease itself.  It then summarizes:


  Thus, the glucose counterregulatory defense against hypoglycemia in
  individuals with diabetes becomes impaired at almost every level and
  rendered even more defective through intensive insulin therapy