One of the things I didn't mention was that I thought she was intentionally hiding behind her support singers in the final moments of the song, which are really powerful. In this video she is coming out of her vocal shell and putting her vocal foot down and nailing the vocals to the wall without their power as a failsafe!
Though I think Kesha has some technical issues that inhibit the freedom of her singing, I think it is nerves that affects her most. It's not uncommon for performers of the highest office to have stage fright - Barbra Streisand for instance - and in ways it's comforting to know that nerves are universal.
How do you hear nervousness manifesting in Kesha's performance? Compare the two videos (the first live performance of 'Praying' can be found down a few threads) looking for evidence.
When can you sense she feels confident?
How do these show up in her singing?