This is not an issue of falling off of a 1/16 height block - if you crouch and move from solid dirt to a lilypad on water at the same level as the lilypad, you will not fall. If you crouch and move towards the edge of a block that is adjacent to a 1/16 block, however, you will fall : not only that, and this is why it is not a duplicate, crouch is then deactivated and will not prevent you from falling off of any other blocks. Once it is deactivated by falling to a 1/16 height block (tested with lilypads, carpets, and so-on) - your crouch is no longer working, and you will fall off of any other block type, despite not manually deactivating the crouch. It appears that the fall that occurs due to moving from a full height block to a 1/16 block adjacent but "below" is enough to deactivate crouching requiring the user to re-engage crouching or simply fall as if one was only walking slowly, not crouching at all.

To test this, on level ground, place one dirt block, and then place a piece of carpet adjacent to it, and then dig a pit adjacent to that.
(RAISED BLOCK) +
CARPET +
\PIT/
If you start by crouching on the carpet, you will not fall into the pit. But if you start on the block higher than the carpet, you will fall to the carpet, and then you can fall into the pit.