When is it time to call for a coaches head to roll?

The night of the loss to the Falcons, I was seeing plenty of posts on this sub about how DC Billy Davis "has to go", or how "he needs to be replaced ASAP."

My question is this: Are a lot of people of the opinion that Davis should be canned for a different defensive coordinator? Are his schemes really subpar? Or were those comments from the minority based on an emotional response to the disappointing loss? This goes for the Chipster as well. He's been head coach since 2013. His first year he got the Birds to 10-6 and to the Wild Card playoff game in a crushing 26-24 loss to the Saints. Last year we started out amazing, but ended up fading towards the end of the season with another 10-6 record. Again, no post-season for the Eagles. If Chip Kelly ended up having us miss the playoffs for the third season in a row this year, do you think it would be time to at least call for an end the Kelly experiment? I personally don't believe so, and 10-6 multiple seasons isn't bad - but I know most Eagles fans are tired of being just "not bad", or "a pretty good team", but never a great team. We certainly don't want to be a team that doesn't make it to the post-season.

Thoughts?

EDIT: Downvoted for asking an important question regarding a lot of comments I saw the other night. Cool.