How can I help my almost 4-year-old, who is grieving for his grandfather?
There are several issues here that are important to address. The first is that children grieve differently than adults and usually for a longer period of time. While your pediatrician may be concerned that your son is still talking about his grandfather, I'm not surprised by it at all. It's part of the normal pattern of grief shown by young children.
Also, it's important to remember that preschoolers have a lot of difficulty recognizing that death is permanent and irreversible. In fact, they may expect the dead person to get up or even ask you how someone will go to the bathroom after they're buried. Again, this is perfectly normal. The adult concept of death is simply too abstract for a child this age to wrap his brain around.
Often we confuse young children by using euphemisms to describe death. We say that someone has "left us" or "moved to a better place" or "gone to heaven." Although these phrases are used with the best of intentions, they encourage a child to expect the dead person to return and can prolong a child's grief.
The first thing you should do is be patient. Hold him in your arms and tell him that you miss his grandfather, too. This lets him know that he is still loved by you even if he has disturbing feelings.
If he stays weepy for the next month, then it would be a good idea to speak with a child psychologist or psychiatrist who can evaluate your son to see if something else is causing his emotional distress.