Problems with the Write Up:
1) As
@Lanefan has noticed, I haven't actually described how to continue as a fighter if you lose the subclass. I probably should as that will be generally useful for other class write ups. It happened in part because I suddenly realized that the rules were really vague about what happened in that case and writing it up exactly would be more convoluted than the original rules make it sound despite being a "normal" 1e AD&D mechanic.
The Cavalier already has basic martial training built in: a 5th-level Cavalier more or less fights like a 5th-level Fighter, other than the differences between weapon-of-choice and specialization. A Cavalier who goes (small-r!) rogue would still have that basic martial training to fall back on and would, one would think, be easily able to carry on as a non-specialized Fighter of the same level using the weapon proficiencies it already has.
What a typical Cavalier doesn't and wouldn't have, though, is a shred of Thief training. In the fiction, you're forcing them to start from scratch as a 0-level Thief, which makes very little in-fiction sense unless you're suggesting - and you aren't, I don't think - that they'd somehow forget all their militia training overnight.
Forcing fallen Rangers to become Thieves makes a bit more sense given that there's already some overlap in abilities (but I'd still make them become Fighters anyway).
3) As written up, Dauntless makes Wisdom a real dump stat for the Cavalier, which is funny but not really the intention. I have considered several alternatives such as capping the Dauntless benefit at +4 or halfing the benefit so that it's only 1/2 your Cavelier level. The important thing is that it isn't as front loaded as the original write up. But I'm not exactly sure where to go with it.
Maybe flip the stat requirements such that they need Wis-11 instead of Int-11 and let Int become their dump stat - they're too dumb to be afraid!
(a long-standing joke here, borne out once or twice in fact, is that on meeting a mounted Cavalier it's an open question which is smarter: the rider, or the mount)
4) The write up is vague on what happens to non-cavaliers below 0 hit points. This is somewhat intended as the rules vary, but how powerful "Hard to Kill" actually is will depend on the rules used at different tables.
Yeah, this is one that, regardless of the actual mechanics used, I'd prefer work the same for everyone in the setting, adventurer or not.
I'm still on the fence about their Martyr action. I'm not sure if it should be immediate death or just they immediately lapse unconscious. I'm equally unsure about what the best saving throw to stay conscious should be. I could see an argument for using a SSS check, a CON check, or a different saving throw.
For staying conscious, we use roll equal-or-under [Con modified by your current h.p.] thus if your Con is 15 and you're at -4 you need to roll 11 or lower to keep going.
5) I would expect some fan of the class to say, "Look what you've done to my boy!" I admit if anything the class is on the weak side now, though it is probably more powerful than most non-specialized fighters. I think I need to tone down the XP requirements after 8th level just a tad.
One thing to watch for, and this the main thing that's made Cavaliers very unpopular to play IME, is that they're
far less useful when unmounted, and most dungeons and adventure sites aren't exactly mount-friendly.