What caused Nacha to die in such an intense moment?
Your question made me smile because the answer is more symbolic than realistic, isn't it? Nacha dies after sampling the icing on the wedding cake containing Tita's tears.
Nacha's story is a sad one. She is the De La Garzas' expert cook from India. She is also a kind of nanny for Tita and loves her like a daughter. Nacha even shares all of her most precious cooking secrets with Tita. It is due to this mother/daughter type connection that Nacha dies. Rosaura is getting married to the man who Mama Elena did not allow Tita to marry. Oh, Tita cries and cries over this! ... As the cook of the wedding cake, Tita cries her tears all into the icing! THIS is the icing that Nacha tastes that leads to her death.
In conclusion, the symbolism here is in the icing. The icing made with Tita's tears symbolizes Tita's hopelessness and sadness in life. Nacha, who truly loves Tita, can no longer survive when "tasting" this type of sadness; therefore, she dies during "such an intense moment."