What do you mean? Aside from Carrhae were there significant cavalry-based defeats Rome suffered? Goldsworthy in his book on the Roman army didn't feel like including more than only a few pages on infantry vs. cavalry combat. He describes cavalry tactics as falling into two categories - missile harassment and shock.

In the small number of pages Goldsworthy devotes to infantry vs. cavalry, he seems to describe an effective Roman infantry. According to Plutarch, during Antony's Parthian campaign the Parthians refused to attack Antony's marching column, and Goldsworthy goes into some depth describing Arrian's defense against Alan heavy cavalry that involved Roman missile harassment of their own - including artillery.

Goldsworthy's book is a little dated now (1996) and draws on Keegan's even older book The Face of Battle. Keegan is very firm in his opinion that cavalry cannot break well disciplined infantry (though I recall some conversations on this subreddit that challenge that position), and this comes through very strongly in Goldsworthy's analysis.

So to the best of my knowledge, I'm afraid the premise of the question is flawed. Roman infantry might be stymied by cavalry (in particular I'm thinking of Caesar's problems with chariots in Britain) but it's not as if cavalry were the hard counter to Roman infantry.

I'm not sure such a "repeating theme" exists at all. What "cavalry based" (to the extent that such a thing exists) armies are you thinking of? The Parthians? Ctesiphon was captured by the Romans five times, and Parthia was at peace with Rome for most of the Principate. The disastrous Parthian campaigns of Antony and Crassus had little to do with some inherent inability of the Romans to adjust to Parthian armies, it was the fault of the leaders--in Antony's case his decision to pursue a Parthian army through Armenia and then retreat during the winter without proper provisions was the source of the majority of his losses, and Crassus' leadership at Carrhae is generally not looked on favorably. The Parthian invasion of Anatolia and Syria, the furthest they ever got, was only initially successful--and it was led by a Roman, Quintus Labienus, and primarily fought with Roman troops, the army of Decidius Saxa, which defected to Labienus after the death of their general. After the initial incursion into Syria the invasion was a total disaster--Publius Ventidius decisively defeated and killed Labienus in 39 and then defeated and killed Orodes' son Pacorus the next year in Syria, at which point the Parthian invasion collapsed. That and Carrhae were the biggest successes of the Parthian army against Rome, and the history of warfare between the Romans and Parthians during the Principate is pretty much entirely a history of the Parthians getting stomped and then making a peace to recover their territory--it's not as though the Parthians were incapable by any means, but to say that there's a "repeating theme" of Parthian victories due to cavalry over the Romans is more than a bit of a stretch

I can't really think who else we might be talking about. The Carthaginians? Other than Hannibal I think we can hardly call their armies "cavalry based," and even Hannibal's army was almost entirely infantry. In any case Hannibal lost, and while he might have had some impressive victories his total inability to make any sort of decisive change in the military situation makes me more than a bit hesitant to classify his victories in this category. Jugurtha? Jugurtha had some impressive initial successes, but was pretty decisively defeated.