The video I posted in My first post on diabetes pointed out that in type one diabetes the person doesn't produce any insulin where as in type two diabetes they produce insulin but the insulin is unable to open the cell to let the glucose in.
Because a type one person doesn't have any islets producing insulin, they cannot reverse their condition. A type two person can though because their body is still producing insulin but it isn't using it properly.
Type one diabetes is an autoimmune disease. This simply means that the body thinks the islets that produce insulin are something foreign and it produces antibodies to kill them off. Once the islets are killed off, there is no more insulin produced.
Read more about autoimmune diseases here