DHT11 Sensor : Stand-by or Shut down ?

I have an ATmega328P monitoring room temperature and humidity. It is enough for me to monitor every 10 seconds. In these 10 seconds, I am putting my Atmega to sleep.

Now , I want to know : Does shutting down the DHT11 for these 10 seconds affect the performance of the sensor in any way or is it advisable to keep it running (stand by) for these 10 seconds ?

[Shutting down means connecting the Vcc of the sensor to GND by means of digitalWrite(Sensor_pin,LOW);]

Also , (The below question is applicable only if your answer to the above question is to keep it in Stand-by) :-

I want to modify the above project such that Temp & Humidity is measured as and when only an input button is pressed.
In this case too, should I keep the DHT11 running?

Is a running DHT11 sensor more accurate than a instantly powered on DHT11 ?

Now , I want to know : Does shutting down the DHT11 for these 10 seconds affect the performance of the sensor in any way or is it advisable to keep it running (stand by) for these 10 seconds ?

Depends on how much time you give the sensor to awake (or better to make a try for a measurement).
As the sensor isn't accurate anyway (it's ultra-cheap, not just for costs but definitely for quality) it's probably almost no problem if you give the sensor about 1 second (that's the minimal time to wait between taking samples) to recover before measuring.

Is a running DHT11 sensor more accurate than a instantly powered on DHT11 ?

As it's quite inaccurate this is probably irrelevant. I guess you won't get a correct value from an instantly powered on DHT11 but I never tried and the datasheet doesn't tell us anything about that. The datasheet is hinting that you have to wait for 1 second to get a measurement but it isn't clear about that (and it's a Google translation from a chinese datasheet).