The princesses were deemed to be immortal because they did not age, but yea, it is never mentioned if they can't be hurt.
In the S2 finale, Celestia was badly hurt in the fight with Chrisalis though, so theoretically they could die, but if she did die, how could she learn about it?
What's to say Luna doesn't die? There never was proof of immortality for the princesses.
The princesses were deemed to be immortal because they did not age, but yea, it is never mentioned if they can't be hurt.
In the S2 finale, Celestia was badly hurt in the fight with Chrisalis though, so theoretically they could die, but if she did die, how could she learn about it?
It doesn't necessarily mean they're immortal if they don't appear to age.
When watching MLP, I do not like to think of two main things:
1) Aging
2) Death
Rainbow Factory
Cupcakes
Sweet Apple Massacre