Program with no BOD, set it to 1.2 MHz internal clock and program ADF in setup mode only (ADF needs to be programmed once in your case).
Feed ATiny13a with 3V3 from ADF board.
PA3FYM As far as I can see ATTINY13A has 9.6 MHz, 4.8 MHz (this I use) & 128 KHz internal clocks.You mean to set 9.6 and use divide by 8? I program it 500 mS after power up. I do not program it again. I power it from 3.3 V from ADF PCB.My opinion is that BOD is required as the problem is due to slow VCC rise due the RC that exist from the long power supply cable. The unreliable operation is that it fails to initialize the ADF most of the times. Once it initialized it works fine with no problems later.