Which is correct:
"but he doesn't" or "but he didn't"?

Some examples from the web:

• She speaks, but he doesn't understand.
• 15 years have passed away, but he doesn't come.
• So now we know Thorwald's coming, but he doesn't.
• Now the doors are open, but he doesn't get in anymore.
• I know that you're dying for a story with the guy, but he doesn't talk to anybody.
• Adam Horner, but he doesn't even look at me.
• [Man #3] His program's fine overall, but he doesn't understand us.
• I told my dad that I bought the stuff, but he doesn't believe me.
• Hard to believe, I know, but he doesn't have a cellphone.
• It's chronic but he doesn't have his medication.
• Audiences love him, but he doesn't come cheap.
• I say stop, but he doesn't.
• Hesaysthatyesterdaymorning he was in the house, but he doesn't have any witnesses.
• You can talk to him, but he doesn't remember much...
• Jesus saves, but he doesn't trust banks.
• David adams, but he doesn't exist.
• His time has already elapsed, but he doesn't knowit yet.
• His brother is married, but he doesn't have children.
• Security cameras caught him, but he doesn't appear in any of our databases.
• Mr Albert said it was professionally developed, but he doesn't think over here.

Some examples from the web:

• Palazzi questioned me for an hour, but he didn't believe what I said.
• A vague description from the sister, hair and fire bits, but he didn't leave any prints here or in the flowerbeds out front.
• Around that time, but he didn't last long.
• He told me to wait two minutes, and I waited, but he didn't come back.
• The gunman could've shot that guy, but he didn't.
• Everyone thought he would, but he didn't.
• Okay, but he didn't.
• Could have jumped but he didn't.
• He should have fired his geology department, but he didn't.
• And then Shirley said, but he didn't.
• On Wednesday, but he didn't.
• I know you trust him and all, but he didn't mention even one of the experimental drugs they're testing right now.
• He was home the evening of the disappearance, but he didn't hear or see anything.
• And he saw the torso wash up, but he didn't see - where it came from.
• The neighbor could've helped you, but he didn't.
• Or flown in the window... but he didn't.
• New York plates, but he didn't get the number.
• The Frenchman was desperate but he didn't say a word.
• I wanted him but he didn't.
• He was corrupt and frivolous, but he didn't deserve that.