I am referring to her letter, about the reception of which I am asking.
So what you do is put the second preposition in front. Syntactically, it works as follows. The basic clause is this:
I am asking about [the reception of [her letter] ].
You can rephrase it thus:
~ About [the reception [of her letter] ] I am asking.
This is an unusual, but valid, word order, sometimes used to put focus on the phrase about the reception of her letter. This phrase is the smallest unit that you can normally move in front of the verb, the constituent about the reception of her letter. You cannot say *about of her letter the reception, nor *the reception of her letter about. For that reason, it is allowed in English to keep this smallest movable unit together at the beginning of the relative clause, even though normally the relative pronoun which needs to be at the beginning of the clause.
The alternative is putting the preposition governed by the verb, i.e. the preposition that heads the adverbial constituent, in its normal position after the verb, separate from its object, the way you did in your example. One of the reasons this is possible in English is in order to avoid about the reception of which, which is sometimes considered a bit awkward.