πολλές φορές διερωτώμαι

I often wonder / I have often wondered.  In this context there is very little difference between the two tenses.

wonder may be better than ask myself here, because the question is not rhetorical.  Cf the three citations of I have often asked myself from the Bank of English:

 deal, and I have often asked myself how I really felt about him.
with them, I have often asked myself `Who is Tony Blair?" It has 
           I HAVE often asked myself what makes a really first-rate conductor

In these cases, I might arrive at an answer simply by thinking about the question.   Compare I often wonder, where the question may be rhetorical or factual (in which case somebody other than the speaker may be able to supply the answer):

                I often wonder if she had a proper babyhood
                I often wonder how it all happened
                I often wonder how his wife feels when she hears about what he did.

and I have often wondered:

I have often wondered whether this mirrors real life.
I have often wondered what happened to the Flower People of the Sixties

             during my career as a doctor, which is now nearly forty years,
I have often wondered what really is the purpose of suffering.

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