Is it permissible to fast for several months as an act of devotion to Allah and as a means of seeking His intercession to fulfill a need, taking into account the virtue of fasting and the acceptance of supplication therein?

There is no harm in continuous fasting for one who is able, as the Prophet, peace and blessings be upon him, said to Hamzah ibn Amr al-Aslami: "Fast if you wish, and break your fast if you wish," which indicates the permissibility of continuous fasting.