So, there are a couple things at play here. As Anna V. noted, he likely represents the sun. Besides the flaming wheel in the sky, a cult title of Apollo is Ixios, apparently from the city of Ixiae, but perhaps also related to Ixion here. However, Apollo and Helios (i.e. the sun) were not originally the same deity, and so the connection there is intriguing but uncertain. Moreover, the name defies attempts at etymology, although the LSJ suggests a possibility with ἱκέτης (hiketēs), meaning "suppliant."
Other ideas for Ixion put forth are related to clouds. Since Ixion laid with a cloud thinking it was Hera, some, such as Martin Nilsson, have speculated that instead of a sun, he was some figure for making it rain. Nilsson also points out that this cloud was connected with Nephele (which is merely Greek for "cloud") in the Argonaut story, where she saves Phrixus and Helle by sending them a ram with golden fleece.
Ixion also must be of extreme antiquity and likely connected to Märchen, as he is completely divorced from any of the major lineages.
There are parallels for him, though. Besides "the sun" or "rain clouds", he is one of the major offenders against the order of Zeus' universe, such as Sisyphus, Tantalus, Asclepius, Atlas, Prometheus, and later Iapetus' two other sons Menoetius and Epimetheus.
Sisyphus might be the closest parallel to Ixion, as one who rolls a rock up the hill and lets it fall back down parallels the rising and fall of the sun, but other interpretations are possible, such as the waves, the tides, the moon even. His sin was to hold death hostage so that no one could die.
Tantalus' crime I outlined here. I do not know what the pool of water below and fruit trees above him mean. It is interesting to note that Pindar thinks his crime was stealing ambrosia (and thus attempting immortality), which parallels not only Sisyphus' crime above, but also Asclepius', who with his medicine could raise the dead. Asclepius wasn't punished in Hades, but outright zapped by lightning (Pindar, Pythian 3).
Their crime however probably reflect Pindar's preoccupation with the hubris of his clientele. After winning fame and glory (kleos is the key word here) in athletic games, they might have developed a big head, and Pindar, suggests Crotty, Kurke, and Nicholson, might have added a tender caution in his praise.
Atlas and Prometheus are both tied in some way to mountains (Prometheus literally), with Atlas at the western edge of the world (the Atlas Mountains in Morocco) and Prometheus in the eastern edge (the Caucasus Mountains).
Hesiod picked up on this and schematized it, making Atlas, Prometheus, Epimetheus, and Menoetius (though a titan, the name is human, and is shared with Patroclus' father in the Iliad, e.g. 16.14), all of which committed some injustice against Zeus which characterizes human condition. Menoetius was full of hubris, and thus Zeus struck him with a thunderbolt. Epimetheus ("afterthought", based on his brother Prometheus, "forethought") of course received Pandora, the first woman and the one who unleashed evils on humankind. (Hesiod, Theogony 507–558 and Works & Days 69–105)
Clay, J. S. 2003. Hesiod's Cosmos. Cambridge.
Crotty, K. 1982. Song and Action: The Victory Odes of Pindar. Baltimore.
Gantz, T. 1993. Early Greek Myth: A Guide to Literary and Artistic Source. Baltimore.
Kurke, L. 1991. Traffic in Praise: Pindar and the Poetics of Social Economy. Berkeley.
Nicholson, N. 2005. Aristocracy and Athletics in Archaic and Classical Greece. Cambridge.
Nilsson, N. The Mycenaean Origin of Greek Mythology. Berkeley.