Is there any rule stating that once a die has been re-rolled, it is locked on that result and can no longer be re-rolled? If a hero has 2 different abilities allowing a reroll, can he reroll the blue attack die with ability 1, then reroll the same blue attack die with ability 2?

The only such limit that exists is that an OL card with the same name cannot be played twice on the same trigger.

A reroll is not a new trigger from the original roll, so an OL cannot play dark fortune to reroll, then dark fortune to reroll a second time.

Because it is not a new trigger, it is worth noting that modifiers carry through rerolls. So, if you pass and OL plays befuddle, then you reroll with lucky charm, it is still +1 shield.

However, for example, Reynhart could use his hero ability, then use his heroic feat if he missed a second time.

For an instance knight can use his skill to reroll defence result, and then use actual shield to reroll it again