I found the following in the MikroTik RouterOS documentation which may bear on this issue. The Reset button functionality was apparently updated/changed in RouterOS v6.47, so some of the documentation we used previously may not work the same now.


From Pages | Getting Started | Netinstall | Etherboot
RouterOS
If your device is able to boot up and you are able to log in, then you can easily put the device into Etherboot mode. To do so, just connect to your device and execute the following command:

/system routerboard settings set boot-device=try-ethernet-once-then-nand

The  boot-device value can also be selected to the try-ethernet-once…  in the RouterOS WebFig pages by selecting   System | RouterBOARD | Settings .   After that either reboot the device or do a power cycle on the device. Next time the device will boot up, then it will first try going into Etherboot mode. Note that after the first boot up, the device will not try going into Etherboot mode and will boot directly from NAND or from the storage type the device is using. 


Etherboot is a mode where the hAP requests new code over the Port 1 Ethernet interface.  It is what we previous did with the Reset button magic.

Based on these words, it appears to me that if you set Boot Device to try-ethernet-once-then-nand, power off your hAP, set up Tiny PXE connected to hAP Port 1 with the appropriate rb.elf file, set Tiny PXE to Online, then just power-on the hAP (NO RESET BUTTON REQUIRED)...it should work.
It did for me when I tried it a few days ago on an NIB hAP ac lite. 

I also used a power-off-reset-power-on technique, but it only takes 14 seconds for the file transfer to start.  I used this technique as well.  See RouterOS documentation 

From Pages | Router OS | Getting Started | Reset Button

Using Reset Button

RouterBOARD devices are fitted with a reset button which has several functions:

• Loading the backup RouterBOOT loader
  Hold this button before applying power, release after three seconds since powering, to load backup boot loader. This might be necessary if the device is not operating because of a failed RouterBOOT upgrade. When you have started the device with the backup loader, you can either set RouterOS to force backup loader in the RouterBOARD settings or have a chance to reinstall the failed RouterBOOT from a ".fwf" file (total 3 seconds)

• Resetting the RouterOS configuration
  Hold this button until LED light starts flashing, release the button to reset RouterOS configuration to default.

• Enabling CAPs mode
  To connect this device to a wireless network managed by CAPsMAN, keep holding the button for 5 more seconds, LED turns solid, release now to turn on CAPs mode. It is also possible to enable CAPs mode via the command line, to do so run the command "/system reset-configuration caps-mode=yes";

• Starting the RouterBOARD in Netinstall mode
  Or keep holding the button for 5 more seconds until LED turns off, then release it to make the RouterBOARD look for Netinstall servers. You can also simply keep the button pressed until the device shows up in the Netinstall program on Windows.
   

Netinstall is a MikroTik app for loading/reloading firmware into their products.  We use Tiny PXE to do that with AREDN First-Install code.

And if you leave the Reformat-Hold-Button time at the default 20 seconds, and hold down Reset waiting for something good to happen with Tiny PXE...

From Pages | RouterOS | Hardware | RouterBOARD | Settings | Mode and Reset Buttons

Mode and Reset buttons

Reset button additional functionality is supported by all MikroTik devices running RouterOS.
...
reformat-hold-button (5s .. 300s; Default: 20s)
As an emergency recovery option, it is possible to reset everything by pressing the button at power-on for longer than reformat-hold-button time, but less than reformat-hold-button-max (new in RouterBOOT 3.38.3).
When you use the button for a complete reset, the following actions are taken:
EXTREMELY DANGEROUS. Use this only if you have lost all access to the device.

1. RouterOS, all of its files and configuration is completely and irreversibly erased by nand re-format;

 

--Tim K5RA