What does "thin-groined" mean?

Flann O'Brien's writings tend to make for interesting discussions due to the many layers he places in his works. As a result, I don't think you will be able to find much consensus on minor details such as what this individual term means. That said, I will do my best to offer my take based on the words and context.

If you read through the entirety of this passage (extending a little beyond both the beginning and the end of the cited portion), O'Brien's language suggests "sorrow", "depression", "weakness", and "faintness of heart" as potential contextual meanings for this term. At the same time, it can also suggest physical weakness as Sweeney (the character speaking) is contrasting himself to stags who have the strength to walk where they wish, but he is forced to forever wander.

This is where your quoted text comes in: Sweeney apologizes to God saying, basically, "Forgive me. I know this pain and sadness is only temporary, but this madness feels worse than death and I do not have the strength to fight it." It's worth noting that "At Swim-to-Birds" is heavily pulled from "The Madness of Sweeney" which means the term "thin-groined" may actually be an approximated translation of something mentioned in the original tale.

For context, "The Madness of Sweeney" takes place after "The Battle of Mag Rath" and tells the story of King Sweeney who was made mad by St. Ronan's curse. Much of the imagery in this reflects aspects of that curse such as how he wanders naked (like the stag), treads lightly like a bird (compared to seagulls), and how he can't keep peace (later mentioned "two hand-shaked cranes", as cranes are known for being territorial, but due to the curse, during the war, he'd regularly break the truce forbidding combat during the evening). As he wanders, like a bird, he'd perch himself in trees frequently. His body even growing feathers in the original tale. His world and life effectively fell away from him and now he is less a man and more a beast, and this passage reflects how he laments that his life has turned out this way.

I hope this in some way helps. I understand this isn't quite a precise answer, but I don't know what would be a better way to answer in regards to a man such as O'Brien's writing.