I was taught that when a woman undergoes her menstrual cycle, she occupies a place of purification that makes her akin to the Divine Mother. Undergoing this purification, the Devatā, being her children, are not worshipped by her.
Gaṇeśa, Śiva and Viṣṇu out of respect do not approach her, and only the Divine Mother herself, her own embodiment, is approachable. The Guru mantra and Iṣṭa mantra, even if belonging to one of the three mentioned divinities, are ALWAYS available to a woman in her menstrual cycle.
Therefore during the cycle you can always perform the mantras of your Guru, Iṣṭa and Devi – they are always available to you as they are attached to your soul, not your body. Do not use the ritual-items such as rosaries or similar during this time as again they are attached to your body, nor your soul. Those initiated by a priest or Guru into the Śiva Pañcakṣari mantra, are also not subjected to this limitation when performing Śiva mantra, as again this is a soul-level initiation.
For other ritual practices, Gaṇeśa and Śiva become available at the closure of the cycle, usually five days from its advent.
Viṣṇu becomes available fifteen days after the cycle has begun.
The Vedic tradition celebrates this divinity in women for 3 days through the annual festival Raja Parva or simply Raja. This occurs upon the entry of the Sun into Gemini, or Mithuna Sankrāntī, and is celebrated especially in Orissa.
During a 40 day or more sadhana, if one is required to take a break due to one’s cycle, then simply continue the penance from where you left off, thus no need to start over.
However, this is all relevant to performing rituals or pūja, whereas personal japa or mantra practice are not restricted at any time for anyone for any form of divinity.