If you are with someone at the moment they take their last breath you are with them because they want you there. If you are not with someone at the moment they died, and you tried very hard to be with them, then they showed their love for you by protecting you from that moment. It sounds strange, but the person who is dying is the one who has a limited amount of control over the moment that they die—not the loved one who is attending to them.
We die a gradual death according to our personality and if that personality is protective then we may protect a person we care about by dying when they are not in the room. We tend to believe that death just happens but, as I have said, gradual death has recognizable dynamics with a process to it. Part of that process is a small window of control over the time that we actually die.
We have enough control to wait until a child, even an adult child, leaves the room. We have enough control to wait until a special person arrives to be with us. I know this seems foreign but there is self-determination over the time that we die, limited, but more than most of us assume. We can take comfort in this knowledge. We can let go of guilty feelings and accept the gift of protection our loved one has given us.