uPD72005 (CAN Controller)

I hear that prior to performing transmit and receive processing, initialization must be performed and that if it is not performed, transmission/reception cannot be performed.
Does this mean that initialization has to be performed just once when the microcontroller starts up, or does it have to be performed each time transmission/reception is performed?

Initialization can be performed just once following power-on.
By the way, it is possible to perform initialization at any time by setting the INIT bit of the CANC register to "1".

Could you describe the count-up method of the receive error counter?
A reception error is detected when the CANBUS line moves from a recessive state of approximately 20 ms to a dominant state of 1 ms, and then returns to a recessive state. The transmission speed is 250 kbps.
[1]In which manner does an error occur and the receive error counter count up?
[2] Does the receive counter exceed 128 during the 1 ms interval of the dominant state?

Regarding the error type, please check CAN error status registers 0 and 1 of the uPD72005 when an error occurs (when an error interrupt occurs).

Regarding [1]
(1) An SOF is recognized when the 1 ms interval of the dominant state begins and reception is performed.
(2) When the dominant state has lasted for 6 continuous bits, a stuff error is detected.
(3) At the 7th bit, an active error frame is output. (REC = +1)
    Moreover, regardless of the fact that an error frame is output, 14-bit dominant is detected. (REC = +8)
(4) Then, every time 8-bit dominant is detected, REC is incremented by 8.
  * The above occurs at over an interval of approx. 80 us.
  * REC: Receive error counter

Regarding [2]
  Since, as described above, REC is incremented by 8 every 8 bits thereafter, so the value of the REC counter exceeds 128 as below.
  920 us / 4 us (250 Kbps) = 230 bits
  230 bits / 8 bits ~= 28 times
  28 times * 8 bits > 128