The metaphor "Se me va a pasar el arroz" alludes in my opinion to the difficulty of determining the right length of time for cooking rice (the literal meaning as someone has already pointed out) and the similarity with knowing when a woman’s fertile years would come to an end, both being imprecise in timing, and both impossible to rectify once gone past the right time.

Although it ultimately has a very similar meaning, the equivalent to the expression "to be left on the shelf would be "quedarse para vestir santos"", at least for Spain.

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Note added at 9 hrs 1 min (2004-09-25 17:00:58 GMT)
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How this would work in a song is another story...