Gastrointestinal loss due to gastric surgery and recurrence: The patient has a history of adenocarcinoma of the stomach, which has recurred after surgery. This could lead to persistent vomiting or gastrointestinal secretions rich in potassium, causing hypokalemia.

Corticosteroid use in palliative care: Corticosteroids are commonly used in palliative care for their anti-inflammatory effects and to improve appetite. However, they can cause hypokalemia as a side effect by increasing renal potassium excretion.
Polymyositis treatment: While the treatment for polymyositis (e.g., corticosteroids) can contribute to hypokalemia, the condition itself might also lead to muscle breakdown, releasing potassium initially, but potentially leading to a complex electrolyte imbalance including hypokalemia during the recovery or chronic phase.
Renal loss due to medication: Certain medications used in palliative care or for the treatment of polymyositis might cause renal potassium loss, contributing to hypokalemia.

Hypomagnesemia: Often associated with hypokalemia, as magnesium deficiency can impair potassium uptake in cells and increase renal potassium excretion. It's crucial to check magnesium levels and treat if necessary.
Adrenal insufficiency: Although less common, given the patient's history of corticosteroid use for palliative care and polymyositis, adrenal insufficiency could occur, leading to hypokalemia among other electrolyte imbalances.

Barter syndrome or Gitelman syndrome: These are rare genetic disorders affecting the kidneys' ability to reabsorb potassium, leading to hypokalemia. They are less likely given the patient's age and presentation but should be considered if other causes are ruled out.
Liddle syndrome: A rare genetic disorder characterized by excessive sodium reabsorption and potassium secretion in the distal nephron, leading to hypokalemia. It's an unlikely cause in this scenario but could be considered in the differential diagnosis if common causes are excluded.