Here's a difficult but useful discussion to have with family members: When do you want to be called? That is to say, do adult children, siblings, and other immediate relatives want to know the minute your loved one seems to be in any new health crisis? Or when the end seems near? Or when?
Knowing their preferences can help eliminate later accusations such as, "Why didn't anybody tell me?" At the same time, it's a burden on a stressed caregiver to have to make a dozen phone calls every time there's a new symptom. Clarifying which circumstances warrant information helps everyone.
Try saying, "Look, Dad's health is stable right now, and this isn't any fun to bring up, but there's bound to be another change in his condition. If that happens, it would help me -- and you -- for me to know whether I should call you. What are your preferences: Do you want me to tell you every time he has a fever or urinary tract infection, just report what happens when we see the doctor, or only let you know about true emergencies when I'd like your input?"
Work out a communication chain to pass along updates, if you haven't already; it helps everyone. You only need to make one call, instead of 20. If you're dealing with relatives eager to know all the details as they happen, consider using e-mail updates, which you can send at your convenience, to convey subtle changes and other information about your loved one.