I don't think you can really argue that his problem is being seen too many times by a lineup. If that was the case, you'd probably see his swing and miss rate drop as the game went on, and that hasn't been the case throughout his career. This graph from brooksbaseball.net doesn't show a steady or even any real decline in whiff rate in the 5th, 6th or 7th innings, when a team would be seeing him for the third time in a game. The only exception is in his change up.
I expected to see a higher walk rate in the 5th inning on, but that actually looks fairly stable. It just seems that batters start hitting him much harder at that point. There's also no real drop in velocity or in the movement on his pitches, which we might expect to see if he was fatiguing.
I'm not sure exactly what's caused his poor results after the 4th inning, but the fact that he's generating swings and misses at about the same rate makes me think that it has more to do with him tiring, despite the fact that his walk rate doesn't go up. In fact, it might be the opposite, as he seems to leave more pitches over the plate as the game goes on... at least until the 7th inning.
Maybe he grows tired and loses his confidence in his ability to hit the corners or come in just off the corners and starts leaving more pitches out over the plate. This would explain why his whiff rate doesn't suffer but his slash line against goes through the roof. Batters still miss his pitches as often, but when they don't, they're getting better pitches to hit.
Anyway, this is a bit of a tangent and this ended up be a long road to saying I get why Farrell would pull him in a close game at 93 pitches. He has a history of the wheels coming off very quickly and while Bailey has struggled, he was taking a risk either way. I don't think it was a particularly good call, but I don't think it was an epically bad one, either. I probably would have let him come out for the 9th and had Bailey ready to go at the first sign of trouble, but I can understand wanting to get Doubront out of there on a good note to build some confidence.