Right now the auction house is down for europe, do auctions time remanining still count down while the auction house is offline or are they paused while the auction house is down?
Yes, the AH auctions still count down when the AH is unavailable.
I noticed this behaviour on the Americas region's AH as I put some auctions up in between two longish AH outages last week. When the AH came back up, the auctions had counted down significantly even though there was probably only 15 minutes between me putting the auctions up and the AH going down.
Edit: Blizzard (relatively) confirmed the behaviour (Source) you see in game by not classing it as a bug:
I can't confirm 100% but I believe it does not pause.