I had never heard the expression "once and again" before!
According to Merriam Webster, it has the following definitions:
once and once more
two or more times
now and again, from time to time, occasionally, sometimes
In the context, it seems to have the third definition - which, until now, I knew as "now and again" (which makes just as little literal sense, when you think about it!) or "once in a while".
It could be the first definition - s/he had had the job once before, and now has it again - but this requires two tenses, meaning the sentence would have to be restructured:
"who had once occupied, and once more occupied..." (or "who had once,
and once more, occupied...")
Similarly, "two or more times" requires "had occupied:
"who had occupied - two or more times - ..."
This dictionary has only one definition for "once and again":
repeatedly, as in "He has been told once and again not to slam the
This just doesn't seem right in the example sentence, as we don't talk about someone "repeatedly" going to work or having a particular job - they just have the job, or work there "once in a while".