I support wmw's original suggestion: "unanswered"
From a theological perspective, no prayer of God's people goes unheard - in fact, if one believes in an omniscient, omnipresent God, no prayer of any sort from any person goes unheard. The problem is when a prayer seemingly goes unanswered. If the prayer is selfish, one can surmise that the prayer was heard and the answer was "no". After all, no good parent would give a child everything the child asked for, because children often want and ask for things that are harmful to them. When a prayer is in accord with God's will, comes from a godly person and yet goes unanswered, even the most pious (in a positive sense) of people can be set to questioning either God's goodness or power.
For Anfechtung, I'm wondering if "challenge" [to one's faith] or "stumbling block" would be a good translation.
The effectual fervent prayer of a righteous man availeth much. (James 5:16, KJV)
Des Gerechten Gebet vermag viel, wenn es ernstlich ist. (James 5:16, Luther 1545)
I'm not certain that "pious" can be used without at least a tinge of irony or sarcasm in English unless the context is pietistic or religiously conservative in nature. Another translation for "fromm" is "godly" - Dictionary: fromm
- so here is my suggestion:
"Die Gebete von Frommen vermögen viel. Aber unerhörte Gebete sind schon eine echte Anfechtung."
The prayers of the godly avail much / are very effective. But unanswered prayers are a stumbling block / represent a true challenge [to faith].