In my campaign players are delivering the invitation to Gwaihir themselves after they saved Balin and returned to Esgaroth. Now my question is what if my players fail in the social encounter with Gwaihir or another Great Eagle and they can't get an audience with Gwaihir or he simply rejects them, what would Balin back in Esgaroth do, what will be his reaction to the players? Will he be angry or understanding?

What do you guys think?

Maybe they now have to do a favour for the Eagles in order to get another shot at an audience?

Or they could just take an Eagle hostage. "Speak to us... or Landroval gets it!"

You could always change the result of a failed social encounter. In other words, rather than being directly presented to Gwaihir, the characters are told he'll be here shortly and the eagles wander off. Gwaihir gets there a week later, he's obviously not interested in what the party has to say, etc. Basically run it as another social encounter with a -TN Modifier because the first attempt failed.

Or tell the party that Gwaihir is busy, but agrees to meet them at Location X (probably a bird-centric ). So the characters have to climb up the heights of a steep mountainside or maybe to the top of a large tree. Otherwise its just like the above though.

I do agree with Garn

One of the things I'd also consider is that for your campain is failure in this encounter okay? If it is then such an outcome is perfectly serviceable, if not then I wouldn't make failure an option (or at least only have it as temporary), instead have differing degrees of success. In such a case you could have the following outcomes:

0 successes - Gwaihir receives the company, but declines the invitation. Eagles do not attend such festivities!

1 to 2 successes - Gwaihir receives the company, and will consider their offer. It's up to the LM as to whether he attends or not.

3 to 4 successes - Gwaihir receives the company, and will attend the festivities.

5 to 6 successes - Gwaihir receives the company, and will attend along with his brother Landroval. He is also impressed with the characters, acknowledging and talking with them during the festival (+ 1 to Standing for each PC).

Good point Rich H. I had kind of forgotten that their can be conditional successes in social encounters.