Seriously, why would you ever leave you're struggling starter in? He's past 100 pitches, given up 6 runs, doesn't have any real command of his pitches, and has been hit fairly hard.
Lets do a risk reward assessment:
Risk:
Very good chance of continuing to struggle, big risk of giving away runs/the lead.
Reward:
Saves the bullpen maybe one inning.
That doesn't look like a very good risk to take to save one of the best bullpens in baseball from pitching 1 more inning.