He was not unusual at all in this respect. I think the study you want is Rosenstein, Imperatores Victi. It's a study of the careers of defeated generals. There very rarely seems to have been long term political consequences for generals who survived military defeats.

Rosenstein argues that this is a result of Rome's particular aristocratic competition and military culture. Here's a bit from his introduction:

But as I will demonstrate in chapter 1, defeated generals suffered no discernible ill effects in the political arena as a consequence of their failures on the battlefield. Very few generals were brought to trial on charges arising out of their defeats. More significant still, the imperatoresvicti as a group went on to win the Republic's most highly coveted and hotly contested offices, the consulate and the censorship, in proportions virtually identical to those of their undefeated peers. Of those who did not, many continued to be prominent in public affairs and enjoy the trust of the senate. The sons of victi gained consulates and praetorships in their turn about as often as the sons of men who had lost no battles. Thus by every conceivable test military failure had no impact at all on the long-term rate of political success of the commanders involved.

It's been awhile since I've read the book. Looking at a few reviews it seems the argument is that to maintain aristocratic competition, opportunities for military command could not be dominated by a few successful generals, and that meant letting people command who weren't very good at it. Blaming the defeated commanders for the defeats would argue against the idea that aristocrats get to run things because aristocrats are just good at running things, so they didn't blame the commanders. Instead they blamed the god (someone forgot to make a sacrifice or something) or the soldiers (if those jarheads had held the line, it would have been fine!) and since the commander wasn't at fault there's no reason he shouldn't continue in public life.

Rosenstein's stats seem in the reviews very convincing. Statistically it is rare that a military defeat ended a public career. People seem to have a more difficult time with his explanation of this observed fact - that Romans didn't blame the commander. Rich in his review says we know Romans did blame commanders - there must be another reason.

When I read the book I was pretty convinced, but since then I've become hesitant to attribute things to a unique Roman culture. I'll have to give it another read and see if I still think it was a convincing explanation.

The counter-examples you mention come from a period in which aristocratic competition had run amok. But even then I don't think these generals committed suicide (except maybe Varus) out of shame. Cato was the high-profile suicide of the civil wars, and he did it out of defiance. I think a similar argument can be made for the tyrannicides. Antony is too much of a romanticized character. I don't know if it's possible to try to give an account of his death that wouldn't basically look like historical fiction.