Summon Monster and the Summon universal monster ability both specify that a creature summoned in that way cannot use its summon ability. Infernal Challenger, however doesn't specify in the description. Is there any reason why the bearded devil can't summon another one during the trial?
1 Answer
Yes, they can.
The spell does not specify that the summoned Bearded Devil cannot use their inate summoning abilities. That rule is specific to Summon Monster and the spells based on it.
It is also not covered by the Conjuration (Summoning) subschool of magic.
Tecnically, the summoned devil can even use his Greater Teleport ability, though it has little use since the creature cannot leave the testing grounds.
However, that is probably an unintended behavior. The purpose of this spell is to create a test where a to-be-hellknight can battle against a devil and the administrators of this test does not need to conjure a real devil (via planar binding) and protect themselves using anti-teleportation spells, nor have to keep re-summoning the devil due to Summon Monster's short duration (in rounds/level).