Can a Chrisitan lose his/her salvation?

[Jehanne]

So, a person can be saved, and yet, not be part of The Elect? 

Yes.

Basically, the non-Elect consists of those persons who were never saved to begin with, or those persons who were saved but later on forfeited their salvation? 

Not necessarily.

You have many religious organizations that practice their own traditions and reject the teaching of the Bible.

Let's take the Catholic church for example.
The Catholic church baptizes in the name of the Father, Son, and Holy Spirit despite the fact that the bible commands to be baptized in the name of Jesus Christ, you wont find anywhere where in the Bible where people were baptized under the titles of Father Son, and Holy Spirit.

Acts 2
Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.

This doesn't mean that a Catholic can't be saved, they just aren't part of the elect, because the bible states that it's not possible for the elect to be deceived. The will live according to the word of God, not some denomination.

How about infants who die in infancy and little children?  Are they part of The Elect?

Only God knows who the "elect' are since he is the one that elected them.

Little children go to heaven, they aren't held accountable for sin, I believe the age one is held accountable is around 16.

So, the Saved set is a proper subset of the Elect set then?

As for the Catholic Church & Baptism, many Protestants (such as Anglicans) baptize using the Trinitarian formula ("In the name of the Father..."); are you saying that they are wrong, also?  And, why should we believe your interpretation of the Bible as opposed to someone else's?  And, does not the end of the Gospel of Matthew state to "Baptize in the name of the Father and of the Son and of the Holy Spirit"? (Matthew 28:19)