ESP-01 Deep Sleep not waking up properly
In the question the OP said:


  I have soldered a wire from GPIO16 to RST.


But, I'm going to post an answer for the people who find this question and need the ESP-01 modification instructions in order to wake an ESP-01 module up from deep-sleep:

The ESP8266 mounted on an ESP-01 board will not wake up from deep-sleep because the ESP8266 wake up signal is not connected to the reset pin of the ESP8266 on an ESP-01 board.  You need to add this connection which can be difficult for most people.  You can see the modification in this picture:

...which comes from this instructables posting. 

If this is too difficult, consider using a different ESP8266 board which brings these ESP8266 pins to board edge connectors.