How to say that a problem has occurred previously in passive voice

Possible answer:

This problem must have been had by people in the past.

The rule is just the same as what counts for any other kind of sentence.

Swap the position of the subject and of the object, then simply put have been after the word must.

Some other examples:

• She must have missed the bus
  • Passive: The bus must have been missed
• John must have experienced bad things
  • Passive: Bad things must have been experienced by John (or happened to John)

Will the following work for you? "This problem must been experienced by people in the past." I suspect that the reason you are having problems using the verb to happen is that it is an intransitive verb.

Well, if you really want the Passive transform of

• People must have had this problem in the past

here it is:

• This problem must have been had in the past by people

which is grammatical English -- people would understand it if you said it,
but not colloquial English -- people might think askance at you if you said it.
Generally the agent phrase by people would get deleted -- it's indefinite to start with, after all.
This leaves

• This problem must have been had in the past

and that is just poor because the idiom is have a/the/some/... problem.

That is, there isn't any real have-ing going on; there is problem-ing instead,
but English doesn't have a verb for that, so we use a construction with the light verb have.
There are many:

• have a baby, have a fit, have a drink, have a problem, have a headache

And moving problem to the other side of have,
and adding an extra auxiliary have by using the Perfect,
and then adding an extra auxiliary been by using the Passive
obscures the idiom, and simply makes it way too complex.

The point of Passive (or any other construction) is to make an utterance more clear.
Not less.

I would say "This seems to be a recurring problem"