A staircase switch is not working as it should. What is cause of the problem?
If the push buttons and the staircase timer are connected with a 2-wire connection, the total working current of the LEDs may be sufficiently high to have its coil be constantly activated.
Adjust the wiring to a 3-wire connection. OR Replace the LEDs with neon lamps (only in push buttons with an E10 lamp base).