Some Catholics currently believe that priests should not be married once they have become a priest. Should this be upheld in all cases?.
First of all, 1 Timothy 4:1-3 says that forbidding people to marry is a doctrine of devils. As long as the Catholic Church does not force its priests to remain unmarried, they are not in violation of this verse.
They Catholic Church should give its priests the choice to marry. Paul says in 1 Corinthians 7:6-9 that if one's gift from God is being able to remain unmarried, then he should be unmarried. But when he cannot contain himself, he should get married, and the Church should follow 1 Corinthians 7:2 and let him marry. If one can remain unmarried, then he will be able to spend more time with God. If one is married, then he is also concerned with the things of this world for his wife according to 1 Corinthians 7:32-35.
There are verses in the bible that show that the leaders of the church can be married (1 Timothy 3:2, Titus 1:5-6). In fact, the rock on which the Catholic Church was built upon, Peter, was himself married (Matthew 8:14, Mark 1:30, Luke 4:38, 1 Corinthians 9:5). In fact, 1 Corinthians 9:5 specifically speaks of many leaders of the young Christian Church being married.
Some people say that because God commanded Adam and Eve to "multiply" in Genesis 1:28 that everyone is to get married, so they can have children and multiply. But this is wrong because Jesus did not get married nor did He have children, so it cannot be a sin to not get married or not to have children because Jesus was sinless.
In conclusion, it is best to be unmarried because the unmarried can devote more time to God. But marry if staying unmarried with lead to fornication and/or burning in hell and allow the married to be the leader of a church, because Jesus accepted it.