Every doctor I've ever talked to about this has seen patients like this -- sadly, sometimes when it was too late to do anything to help them. Hopefully this won't be the case with your husband.
Only your husband could say why he won't admit his problems and seek help for them (if, in fact, he's even thought about this). Sometimes the problem is fear -- fear of what might be found, or fear of what might need to be done to treat it. Sometimes the problem is embarrassment. And sometimes the problem is pride -- an unwillingness to admit any weakness, and a determination to "tough it out" regardless of the problem or its consequences.
Whatever the reasons, I hope your husband will face them honestly and seek whatever medical help he needs. God gave our bodies to us, and He wants us to take care of them. Many of the laws in the Old Testament had to do with healthy living, and they were part of God's will for His people. In light of Christ's sacrifice of His body for us, the Bible commands us to "offer your bodies as a living sacrifice, holy and pleasing to God" (Romans 12:1).
Pray for your husband, and pray, too, that God will give you wisdom in dealing with him about this. Don't nag him, but let him know you love him, and because you love him you want him to get the help he needs. In addition, recruit other members of the family to encourage him to overcome his reluctance.