If the answering of supplications is guaranteed (according to the conditions of the Hadith), then why are there times when supplication is recommended, or Hadiths such as "the supplication of the wronged has no veil between it and Allah"?

Designating specific times or states for the acceptance of supplication means that supplication during these times is more likely to be accepted, not that the desired outcome is guaranteed to occur at these times, or that supplication will not be answered at other times. It has been reported that it is desirable to seek out supplication in these noble instances, such as the last third of the night, the Day of Arafah, the Day of Jumu'ah (Friday), the time of dawn, and between the Adhan (call to prayer) and the Iqamah (second call to prayer).

The fact that these times are occasions for acceptance does not mean that the desired outcome will inevitably occur in every case. This may not happen due to a flaw in the conditions of supplication, or the supplicant's impatience, or if the supplication involves sin, or if the answer is delayed for the servant's benefit. Allah Almighty has promised to answer supplication absolutely at all times, and the designation of certain instances indicates the increased certainty of acceptance therein, not that acceptance is restricted to them.