The short: Protactinium is a holy terror.
In a thorium reactor, the reaction goes:
232Th+n -> 233Th -> 233Pa -> 233U
with side reactions involving 231Pa and 232Pa, which go on to make 232U
That "233Pa" is protactinium. When enriching uranium to make plutonium, the reaction goes:
238U+n -> 239Np -> 239Pu
The reactions are more or less the same: We make an intermediate, which decays to our fissile material. 239Np has a half-life of two days, so it decays quickly, and it won't capture any more neutrons, meaning we can keep it in the reactor core.
233Pa has a half life of 27 days and it'll capture more neutrons, poisoning the reactor. It'll form 234Pa, which decays to 234U, none of which you want in your reactor.
This means you have to move the 233Pa out of your reactor core, and the only sensible way is in the liquid state, so the molten sodium reactor (MSR). It's not that "MSRs work very well with Thorium", it's that "If you're gonna use thorium, you damn well better do it in liquid". So at this point, we have our 233Pa decaying to 233U in a tank somewhere, right?
233Pa has a radioactivity of 769TBq/g (terabecquerels per gram) and that's an awful, awful lot. It also decays via gamma emission, which is very hard to contain. The dose rate at one metre from one gram of 233Pa is 21 Sieverts per hour. That's a terrorising amount of radioactivity. That's, if a component has a fine smear (1 milligram) of 233Pa anywhere on it, someone working with that component has reached his annual exposure limit in one hour.
Compounding this, MSRs are notoriously leaky. That 233Pa is going to end up leaking somewhere. It's like a Three Mile Island scale radiological problem constantly.
The liquid fluoride thorium reactor, LFTR, proposed by Kirk Sorensen, might be viable. It comes close to addressing the Pa233 problem and acknowledges that the Pa231 problem is worrying, but no more so than waste from a conventional light-water reactor.
The thorium cycle involves the intermediate step of protactinium, which is virtually impossible to safely handle. Nothing here is an engineering limit, or something needing research. It's natural physical characteristics.
(Bulletin of the Atomic Scientists, 2018: https://thebulletin.org/2018/08/thorium-power-has-a-protactinium-problem/ )