Yes, it's closer to medical insurance. You will probably find it very difficult to get a new policy now, given your father's condition, so i'd investigate any possibilities of existing cover in places you may not have thought of - such as credit cards.
In general I think you can purchase travel insurance at any time, but coverage won't be retrospective AND they'll look hard at any claim to see whether you took out the insurance in good faith.
The issue you have to consider, though we all hope it won't happen, is the possibility of a forced medical evacuation.