Mahabharata, in which the snake sacrifice was mentioned first, did not describe anything about Agni cursing Veda mantras to become ineffective.
The following is the extract from Mahabharata, where the final part of the snake sacrifice was described.
"Sauti said, 'Listen now to another very wonderful incident in
connection with Astika. When king Janamejaya was about to gratify
Astika by granting the boon, the snake (Takshaka), thrown off Indra's
hands, remained in mid air without actually falling. King Janamejaya
thereupon became curious, for Takshaka, afflicted with fear, did not
at once fall into the fire although libations were poured in proper
form into the blazing sacrificial Agni in his name.'
"Saunaka said, 'Was it, O Suta, that the mantras of those wise
Brahmanas were not potent; since Takshaka did not fall into the fire?'
"Sauti replied, 'Unto the unconscious Takshaka, that best of snakes,
after he had been cast off Indra's hands, Astika had thrice said,
'Stay,' 'Stay,' 'Stay.' And he succeeded in staying in the skies,
with afflicted heart, like a person somehow staying between the welkin
and the earth.
"The king then, on being repeatedly urged by his Sadasyas, said,
'Let it be done as Astika hath said. Let the sacrifice be ended, let
the snakes be safe, let this Astika also be gratified, O Suta, thy
words also be true.' When the boon was granted to Astika, plaudits
expressive of joy rang through the air. Thus the sacrifice of the son
of Parikshit--that king of the Pandava race--came to an end. The king
Janamejaya of the Bharata race was himself pleased, and on the Ritwiks
with the Sadasyas, and on all who had come there, the king, bestowed
money by hundreds and thousands. And unto Suta Lohitaksha--conversant
with the rules of building and foundations--who had at the
commencement said that a Brahmana would be the cause of the
interruption of the snake-sacrifice, the king gave much wealth.
The king, of uncommon kindness, also gave him various things, with
food and wearing apparel, according to his desire, and became very
much pleased. Then he concluded his sacrifice according to the
prescribed rites, and after treating him with every respect, the king
in joy sent home the wise Astika exceedingly gratified, for he had
attained his object. And the king said unto him, 'Thou must come again
to become a Sadasya in my great Horse-sacrifice.' And Astika said,
'yes' and then returned home in great joy, having achieved his great
end after gratifying the monarch. And returning in joy to his uncle
and mother and touching their feet, he recounted to them everything as
it had happened.'
So this story must be from folklore or an interpolated story.
Further, Rig Veda I.164.46 says, Agni is the BRAHMAN.
They call him Indra, Mitra, Varuna, Agni, and he is heavenly
To what is One, sages give many a title they call it Agni, Yama, Matarisvan.
The BRAHMAN cannot and will not curse Vedic mantras to become ineffective.