This exact question has been raised in the Govinda Bhashya of Baladeva Vidyabhushana. (Please note that this translation often uses the word "demigod" in place of "deva." Also, keep in mind that in this bhashya of the Brahma Sutras, Vishnu is revered as Brahman.):
The objector may say: "[...] There remains, however, a contradiction in the description of the words of the Vedas. Before the birth and after the death of each demigod, a period
would exist when the name of that demigod would not have any meaning. At that time the words of the Vedas would become meaningless, like the statement ‘the son of a barren woman.’ In this way this idea is refuted. The Mīmāṁsā-Sūtra says: autpattikas tu śabdenārthasya sambandhaḥ: ‘In the Vedas the relation between name and the object named is eternal.’ This idea [that the devas are embodied souls] would then contradict the eternality of the names in the Vedas.”
If this objection is raised, then he [Vyāsa] replies:
[If someone objects that this idea is inconsistent with the eternal nature of] the words in the Vedas, then I say no, because of [the description of] the creation [of the world, and also because of the evidence given] in śruti and smṛti. [Sutra 1.3.28]
The creation of the material bodies of the devas and other beings in the universe is done by Lord Brahmā, remembering their eternal, archetypal forms recorded in the statements of the Vedas. These archetypal forms are eternal, and existed before any of the bodies of the living entities were manifested. [...] The Vedic words describing the devas and other kinds of living entities are not names of specific individuals, but of certain classes of living entities, just as the word “cow” is the name of a certain kind of living entity.
“By reciting the words of the Vedas in the beginning, Lord Brahmā created the names and
forms of the material elements, the rituals, the devas, and all other living entities.” [Vishnu Purana 1.5.64]
And therefore the eternity [of the Veda is proved]. [Sutra 1.3.29]
The eternity of the Vedas is proved by the fact that the creator Lord Brahmā creates the world by reciting the Vedic words describing the eternal forms and by remembering the previous creation. Kaṭhaka Muni and the other sages should be understood to be merely the speakers and not the authors of the Vedas. It is stated in the Brahmāṇḍa Purāṇa:
“**The Vedas, in their entirety, are eternal, enduring, and present in the mind of Viṣṇu; in creation after creation, they are brought up as they are, with the same order, same characters and the same notes, never otherwise. [...] The objection may be raised: “So be it. The śruti explains that by remembering the words of the Vedas Lord Brahmā creates the forms of the devas and other living entities. This may be in the case after the partial cosmic devastation [naimittika], but how can this method of creation be employed after the complete cosmic devastation [prākṛta], when absolutely everything is destroyed, and how can the Vedas be eternal under the circumstances of such complete destruction?”
If this is said, then he replies:
Because the names and forms remain the same even at the beginning of a new creation,
there is no contradiction. This is proved by śruti and smṛti. [Sutra 1.3.30]
The core of the meaning is “Because the previously spoken names and forms remain the same.” At the time of the great cosmic devastation, the eternal Vedas and the eternal archetypal forms described by the Vedas enter Lord Hari, the master of transcendental potencies, and rest within Him, becoming one with Him. At the time of the next creation they again become manifested from the Lord. Lord Hari and the four-faced demigod Brahmā both precede their acts of creation with recitation of Vedic mantras, which leads to meditation on the archetypal forms. At the time of a new creation, the Creator remembers what He created in the previous creation, and He again creates as He did before. This is like a potter, who by saying the word “pot” remembers the forms of pots he previously fashioned, and goes on to make another pot just like them. The process of creation after the partial cosmic devastation, and also after the complete cosmic devastation, is performed in this way.
The smṛti says:
nyagrodhaḥ su-mahān alpe
yathā bīje vyavasthitaḥ
samyame viśvam akhilam
bīja-bhūte yathā tvayi
“O Lord, just as a great banyan tree rests within a tiny seed, in the same way at the time of cosmic devastation the entire universe rests within You, the seed from which it originally sprouted.” [Viṣṇu Purāṇa]
Everything has been explained clearly, so I will not have to really elaborate. In summary, the main idea is that the Vedas are a blueprint for archetypal forms of the devas, so the creation or destruction of individual devas within the universe do not at all contradict the position that the Vedas are eternal.
