The cause is unknown, but sometimes on entities with logic clocks - particularly ones that use rail devices and other things to surpass the normal clock limit - doors and logic blocks will stop responding to player input for a period of time. However, entering cores, destroying, and adding blocks on the entity still works.
The unresponsive period seems to depend on how long the clock keeps running, and possibly server load.
During a desynchronized period, pressing Tab-F6 will force the game to load the correct block states. (However, the unresponsiveness continues even after pressing Tab-F6.)