Men who work in what are considered "Blue Collar" jobs often remove their wedding rings while at work, because a ring could easily get caught on manchinery and potentially rip his finger off. I'm assuming you'd like your man to be uninjured.
Same type of thing for those in the medical and scientific fields- the ring could cause a problem - a place for germs to collect, an element that could react with chemical compounds and drastically alter the compound.
My spouse rarely wears his wedding ring because he is allergic to all metals; his ring is pure silver and even that will cause irritation, rash and raw open sores on his finger if left on long enough.
Have you asked your spouse why he takes his ring off? Are you naturally suspiscious of his behavior when he is not with you? Does the issue of the ring - the fact that it IS an issue - say more about him or about YOU?
trust is an essential element in the marriage - without it, you don't truly have a marriage. Learn to trust your husband and aslo work on your self esteem so that you do feel worthy of him and his affection - when you feel good about yourself, you don't worry so much about other people's innocent actions.
A ring is not the marriage - love, trust, mutual respect is the marriage. I love, trust and respect my husband enough to NOT insist he wear a ring that causes him problems. After all, it's my bed he comes to every night, my arms he comes to for comfort, and with whom he discusses his most intimate issues. I have no worries.