The so-called problem of unanswered prayer is a familiar issue in Christian apologetics. It's not just a philosophical or theological issue, but a practical issue–inasmuch as many believers find unanswered prayer aggravating. In some cases that leads to loss of faith.
I'd simply point out that the "problem of unanswered prayer" isn't distinctive to prayer. It's not a special problem that's confined to prayer. Rather, it's a subdivision of a general issue regarding the mystery of divine providence. Why is it so often the case that the righteous suffer while the wicked prosper? Why does the distribution of weal and woe so often seem to be random?
Insofar as Christian theodicy has a general explanation for the mystery of providence, that's applicable to the "problem of unanswered prayer" in particular. Put another way, the experience of unanswered prayer isn't surprising. Rather, that's to be expected given the mystery of providence. However frustrating unanswered prayer may be, that's not unique to prayer. If you think about it, there's no specific "problem of unanswered prayer". Unanswered prayer doesn't raise any new issues. Unanswered prayer doesn't create a problem that's not already on the table in reference to the broader question of divine providence. Same pattern on a lower scale.