I have recently run into issues with the DHT11. It turns out that the issue is the time that a call to pinMode takes in the DHT11 library. In a small program pinMode returns as fast as 2.5-5 microseconds. In my large program it can take as long as 37 microseconds!!! This causes the code to overrun the timing at the start of the sequence when telling the DHT11 to start sending data. A call to expectPulse(LOW) finds that the line has already gone high and returns 0 immediately. The mainline code interprets this as a timeout (which also returns 0 from expectPulse()).
My initial response was to edit the code to change some of the timings but it was hard to make it correct for both the small program (fast execution) and large program (slow).
However, I recently discovered that the ESP8266 has fast instruction RAM (IRAM) and slower flash storage. I suspected that the routines are being pushed out of IRAM & consequently slowing down quite badly. So I modified the DHT.CPP to include a directive to ensure that the two timing critical routines (DHT::read and DHT::expectPulse) were both run from IRAM…
CODE:
SELECT ALLboolean __attribute__((section(".iram.text"))) DHT::read(bool force) { ...
and
uint32_t __attribute__((section(".iram.text"))) DHT::expectPulse(bool level) {...
So far, no more problems! 
As soon as I unplug the USB cable and re-connect, the device goes back into configuration mode.