Many believers consider that for someone to be an apostle they must have personally seen Jesus. This is not necessary.
This concept of having to personally see Jesus comes from two scriptures, which at face value seem to indicate this. Acts 1:21-22 discusses the selecting of the 12th apostle to replace Judas and says that, "one of these must become a witness with us of his resurrection." People therefore think that an apostle must personally have witnessed or seen Jesus to qualify.
Also in 1 Corinthians 9:1 Paul says when defending or qualifying himself that, "Am I not free? Am I not an apostle? Have I not seen Jesus our Lord? Are you not the result of my work in the Lord?"
Explanation of those Passages
Jesus initially appointed 12 apostles, but later on when he ascended (Eph 4:7) he gave gifts to the Body of Christ, which included the gift of apostles. (Eph 4:11) The Bible is clear that we need apostles and there would be a number of them, however the 12 apostles were specifically needed for a certain task which included the founding of the Church. Of this it was said that Judas' replacement (Matthias) must be a witness with us.
The Acts passage is not saying that to be an apostle each person must personally witness Christ. We know because later in the Scriptures other apostles are mentioned who were from other places, and were not personal witnesses of Christ's death and resurrection. Examples of apostles who were not even Jewish are Andronicas and Junias (Romans 16:7)and also Timothy and Silas (1 Thess 2:6 mentioned indirectly). Matthias was chosen to replace Judas, and was someone who was needed to fill in a specific gap.
In the Corinthians passage, Paul is giving a list of reasons of his suitability - he is making a defence of himself to others who have accused him. He uses various arguments including the facts that he saw the Lord, and was also an apostle. There is no linking of the two points but rather just stating a list of reasons. Paul is not an apostle because he saw the Lord, rather he saw the Lord, and he was also an apostle.
It does seem that many apostles do have close encounters with Christ. Today it is the same with apostles. God calls, equips and trains people to do His will wherever and however He wants. We are not saying apostles haven't seen Christ, but we are explaining that God can call them without appearing to them, even though He often does. Ultimately it will be the way Christ chooses.