I’m not a network expert either but I agree that connecting the mac to the extender should keep most things local so that does put a dent in the “flakey network” suspicion. It may still be worth ruling it out and it looks like you can get the OS to start-up in Access Point mode by pressing Button 2 while holding down Button 3. You should then be able to connect to the access point (the SSID is displayed on the OS LCD) from your phone’s wifi settings and use the phone’s browser to view the wifi config page (the IP to browse is also on the OS LCD). You can then enter the main wifi SSID and password, save and reboot. Please export and save the OS config before doing this!
So the Arduino and OSPi versions will reset themselves if they detect persistent network failures and/or if the software gets stuck (i.e. they have a watchdog timer). I know the ESP8266 has a watchdog timer so that could be triggering the reset if the code freezes for some reason.
I do wonder if your OS is in fact regularly resetting without being noticed, not just when querying log records. One thing I have setup is IFTTT integration where my OSPi will generate an SMS message whenever it reboots. This link shows how to setup and could be informative. Getting to the bottom of the barrel here, but a poor power supply could potentially cause a reset during heavy wifi activity. Are you using one provided with the OS or did you source independent. How many amps is it rated for?