Indian authors distinguish between fixed (nitya), occasional (naimittika) and optional (kāmya) sacrifices. The role of desire in the latter ones is obvious: one would not perform a sacrifice for rain, unless s/he desired rain. So, the agent of the vṛṣṭikāmeṣṭi is "one who is desirous of rain". On the other hand, the first and the second kind of sacrifices are usually described as mandatory, regardless of what one might or might not desire. The agnihotra, a typical example of the first kind, is to be performed daily throughout one's life. The jātakarman, an example of the second kind, is compulsory required at the birth of a son. The agent of these two kinds of sacrifice seems to operate independently of desire, just for the sake of obeying the Veda.
But, in fact, the Mīmāṃsā understanding of the agent of sacrifices is the same in all cases. Fixed rituals are to be performed throughout one's life because their agent is identified as "one who is desirous of heaven". And heaven (svarga), explains Śabara means "happiness", and everyone longs for happiness. So, the reason why the agnihotra is a fixed ritual is that the condition for performing it will never cease. One will desire happiness until her very last day, and that is why s/he is bound to perform it until her/his very last day.
But what about the case where a specific sacrificer is supplied, but no hint of a desire is left (e.g., in occasional rituals, with formulas like "the one whose son was just born should perform the ritual …")? In order to make sense of these cases, Rāmānujācārya (and other authors?) has to abandon his usual Mīmāṃsā 'down-to-earth' attitude. In TR IV §10.11 he answers that the very non-performance of a prescribed duty is, for cultivated people, something one has to desire to avoid: "In fact, dharma is also one of the human purposes (puruṣārtha)". In saying so, Rāmānujācārya interprets artha as goal and connects it automatically with one's natural desire.
More in general, since heaven is explicitly (see Matilal 1986) stated to be a soul’s condition and not a physical place, a “stoical” way out telling us that the fulfilment of one’s duty causes a man to be happy, is always possible.