I heard that if during forty days I perform some special ibaa'dah continuously (for example saying tasbih "subhanallah va bihamdih" one hundred times every morning and evening), it becomes wajib for me, and that I can't quit it after forty days. Is that true?

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

What you heard is not true. But what is better for the person is to choose a good act and not disrupt it. Muslim reported from Aisha (RAA) that she said: 'The Prophet (Sallallahu Alaihi wa Sallam) was asked about the deed that Allah likes most. He replied: The deed that lasts no matter how small it is.'
Allah knows best.