If you attempt to use a fallingsand clock or a fill clock inside of spawn chunks and everyone disconnects from the server or all moves to another world the clock fails to run. It appears to me that spawn chunks stop processing redstone and command blocks when there are no players present in the main world.

How to recreate:
Place a command block in the spawn chunks with this command and then place a redstone_block directly on top. Then simply log out of the server (be sure no one else is online), come back to see the clock has stopped running.

summon FallingSand ~ ~0.5 ~ {Block:redstone_block,Motion:[0.0,0.35,0.0]}

What should happen:
The clock should have continued running while the server was empty, you should re-login to see the clock still triggering.