Hi Daniel,
Another HC08 to S08 difference here is that the S08 will only show the last reset status whereas the reset causes can accumulate in a HC08 if it is not cleared by reading.
The S08 can have multiple bits set if multiple sources were present at reset.
You only need to check the SRSR on initialisation, reading from it later makes no sense. Also doing it this way, the fact that it is not resettable is irrelevant.