How can I convince Dad to see a doctor?
From what you say, it sounds like he does not want you to be aware of his difficulties. This could be because he wants to protect you, it could be part of him refusing to acknowledge even to himself that there may be something wrong with his health, or he may be making a choice that he doesn't want to know what is causing his stomach problems. Whatever the reason, it sounds like there is little you can accomplish dealing with him over the phone or via e-mail. You tried that route and seem to have struck out. I presume your mother has also attempted to have frank discussions with him, without success. I would suggest you have a discussion with all the close family members. As a group, it may be helpful to talk about who he is most likely to listen to. Who has been able to help him deal with any conflict in the past? I would suggest that person have a face to face encounter with him in the very near future. That person should express their concern, ask him why he is not getting properly diagnosed and treated and see what he says. I would suggest keeping the conversation gentle and caring. He may not respond to the first discussion, but with continuing symptoms and a positive discussion, he is likely to follow-up shortly.
One other thing to consider is whether the doctor has done a good job explaining the issues to your father. Does this doctor have a good relationship with him? Is the doctor sensitive and kind? Did the doctor listen to any concerns your father may have expressed? Perhaps a visit with a different doctor would be helpful. It might be helpful to have the family person he is most likely to listen to, go with him to the doctor. They could then discuss what they heard and hopefully together, make a decision in his best interest.