By comparing a qualifying lap time to a race lap time, you are not comparing like for like.
In qualifying, the teams turn up their engines to give maximum performance. It is not possible to do this during a race as you would likely break the engine due to the excessive revs/power being produced for the full race distance of around 200 miles.
Also during qualifying the cars have fresh tyres (and the quickest tyres ie softest) as well as very low fuel loads. This makes them as quick as possible for the lap or two that is required to set a qualifying time.
Fuel load is crucial, a fully laden car carries up to 100 KG of fuel at the start of the race, meaning an average lap penalty of about 3-4 seconds - every 3kg of fuel carried adds about a tenth of a second per lap, depending on the circuit.
So at the start of a race, when the tyres are in good condition, the cars are heavy and so cannot get near their times from qualifying. As the fuel load comes down, the tyres are wearing out so once again lap times cannot compete with those in qualifying.
Most cars will change tyres once or twice per race, so the cars are usually fastest after their final pit-stops when the fuel load is relatively light and they have fresh tyres. But even then, they will be carrying 20 Kg or so of fuel so times are still off what they were in qualifying. Added to that the fact the engines are "turned down" to reduce the chance of a failure, you can see why qualifying lap times are not usually beaten during a race.
Finally, with the 2016 regulations, drivers can use their DRS (Drag Reduction System) whenever they like, but in the race they can only use this on the designated straight(s) when they are within 1 second of the car in front. This can account for around 1 second per lap.