Found the problem!!!!
As u can see here: homesp.cz, almost 3 hours with no problem 
The module was closing the connection so fast after HTTP request was sent. I added this line of code
while(!client.available()) delay(1);
right after sending HTTP request and everything goes well! Just need to wait for server response, then i can send my module to sleep.
I dont even need to disconnect from wifi or stopping the client. Average time while the module is wake is 1800ms which is really great.
Thanks so much for your time tho!