'Raisons de la demande' means '(state the) reasons of the demand'
de raisons de sourire
"Je vous déteste pour beaucoup de raisons mais je vous aime sans raison" is "I hate you for a lot of reasons but I love you without reason".
It means, "We sent the request to your manager again.".
ce type de discipline demande de l'entrainement
It means Asks them to learn
une demande de congés.
Ask them to give you the information (you require).
It a letter asking for information
ce genre de discipline demande de l'entraînement
De tu means: of your in English.
The indefinite article "de" in Spanish is analogous to the indefinite article "of" in English.
"You can, if you wish so, tell us the reasons for your dis-inscription (termination of you inscription)"