How is your power supply to your ESP? Have you tried adding a capacitor across the power supply to the ESP? In my case it worked miracles because the ESP uses lots of power when transmitting (up to 400mA if I’m right) and a small capacitor will handle that better. 100uF or something similar small will do the trick.
Basically, wifi is notoriously unreliable. The ESP has a very small antenna and works in the overcrowded, overpopulated 2,4Ghz frequency. If you live in an area (such as myself) with lots of other 2.4Ghz transmitters/receivers it can do a lot of damage to the signal quality because wifi is a half duplex medium, unlike ethernet.
So it could be why your ESP is disconnecting, but your tablet works fine with your accesspoint/router because it probably has a better chip and/or antenna. Have you tried moving the ESP a bit closer to your accesspoint or reconfiguring your accesspoint to the least used channel? You can use a tool like inSSIDer to check for least used channels in your vicinity.
No, others have issues with this too, Usually it’s power related. Have you tried the capacitor? In my case that helped a lot. It could also be a faulty module, they are really cheap after all. It may be worth trying another ESP.
I had/have the same problem one thing that reduced the disconnections for me was adding a 1-3 ms delay in the main loop maybe that gives the esp more time to work?? no idea really. but now i am getting esp disconnections 1 time in 10 min max.
The delay in the main loop does not work, only to lose sensitivity.
But in the process of timer is much better. I did 10 seconds.
Problem with disconneted stopped.