Yes - they suddenly go dead, which is why I carry a new spare with any horn I use them on. Still, that's just a data point, not a condemnation. In fact, a gradual death like a cane reed would probably be worse for the player because the fact that the reed is dying sort of creeps up on you. Three weeks on tour for any reed is pretty good - its a lot less trouble to use one reed for three weeks than it is to juggle a box of five cane reeds for that same period, especially on the road. Plus, the repeatability of any synthetic reed compared to the variability of five cane reeds is an added plus.
Consistency is the greatest factor with the synthetics. If you can find one you like, and take care of it properly, your horn is going to respond exactly the same night after night. This is a tremendous advantage because you are not having to 'chase' the cane reed as it goes through changes through the night. Every time you pick up the horn you know exactly what you are going to get. Plus, you tune up at sound check, put the horn down and go to dinner, pick it up three hours later and play - just like it was when you put it down. I am loving this aspect of the syn reeds with my 'doubles' (alto and baritone).