@György-Farkas it was about 2h 30min, most of time it was idle. I consider to put there QI receiver coil for wireless charge. Actually the lack of hibernation or sleep mode could be potential problem in future.
my Omega2+ will "shut down". I can't access the Wifi AP and the LED is off.
If you find your board in the state you described again, before you do anything with it try probing the SPI lines with a logic analyzer. If you see activity it means that your Omega2+ suffered an unexpected reboot and the SoC primary bootloader is trying to load U-Boot using 3-byte addressing, but the SPI flash is still configured to use 4-byte addressing. (refer to Omega2 reboot for more info on this issue). If this is the case you have to power-cycle the board in order to get it to boot again (which resets the SPI flash addressing to 3-byte mode)
@Sergey-Suyazov We strongly recommend using a Dock to provide power to your Omega. Improvised power supplies usually can't keep up with the Omega's sudden changes in current requirement caused by the WiFi radio. This would explain the instability you're seeing with networking.
The LD1117S33 (if authentic) needs minimum of input 0.1uF and output 10uF capacitors.
Also, do not use thin power supply wires. I recommend minimum of 22 Ga.
Okay, I added 47uF and 220uF capacitors to my circuit (on Vin and Vout of the LD1117 respectively) and swapped all the wires for 22 gauge. And... it works! Boots up completely and was able to setup wifi through web config and so on. Thank you!
Omega2 requires solid 3.3V stable voltage output at 300mA.
And one more critical spec... power supply needs to be able to handle in-rush current during WiFi power-up without voltage drop.
That fleabay $0.99 item needs a large capacitor (I recommend 220uF 6.3V) on its input side and a large capacitor on its output side (I recommend 470uF 6.3V.) The link between that unit and Omega 2 cannot be too thin gauge (I recommend 22 ga) and definitely use soldering as opposed to using DuPoint connectors.
That seems highly implausible, as the MT7688 isn't really designed for battery operated systems.
What you should probably do is use a microcontroller intended for ultra low power / sleep mode / wake on interrupt operation.
Have that occasionally power up the MT7688 (USB power switch, regulator with enable, etc) when it needs wifi. Make sure you either have no persistent file system state, or do an orderly shutdown each time.
Also consider if there may be another wifi solution that is a better fit for your application.