In order to enhance the battery life, the remote goes to sleep when it is stationary. The Control Center remote has an accelerometer built in to detect activity. Even slightest movement of the remote (picking it up, for example) wakes up the remote.
You can change this behavior by navigating to Settings > Remote and enabling Enhanced Sensitivity. If the button says, "Enhanced sensitivity", this feature is disabled. Enabling it will keep the remote awake and not allow it to go into a sleep state meaning you won't have to wake it up.
Note: With Enhanced Sensitivity enabled, your remotes battery life will be affected.
Expert tip: The remote will not control the main unit when it is sleeping. If you try to use it on a table, after it has been sitting for a while, the remote will likely not respond until you wake it. Just give it a small shake or pick it up before use.
