We call Jesus the son of God that became the son of man. And yet, Jesus is God per the doctrine of the trinity. Why don't orthodox Christians address him as God when talking about him and praying? Is there a biblical basis?
The evolved and gradual revealing of the deity starts out with the concept of 'God' based on original words that imply power. God was a word secular society also used. It seems to mean the divine being, regardless of wether he is the true God or not. The Bible defines this divine being as actually only One, that is in contrast to all the many gods of the pagans. The concept developed at the time of Moses is that this 'God' is Jehovah (or Lord) which means I AM, the One God defined as he who alone is eternally before all things.
As we find the concept of the trinity more fully developed upon the actual appearance of the Son in the flesh, the name Lord is transferred to Christ so that Jesus takes the title Lord, that is the One and only God. Therefore if we pray 'Dear Lord Jesus' we are praying 'dear the one and only God - Jesus.'
However in the clear light of the trinity the word 'God' is generally used to refer to the initial more ancient conception of God as the original powerful one. God is therefore usually pertaining to the Father. The reason why the Father is most often associated with 'God' is because the Father is in a sense the 'originating person' of the eternal trinity, whom the Son proceeds from. The Son is like the word 'proceeding' 'from' the Father.
As our prayers are more frequently made to the Father, we often say 'Dear God' meaning 'Father'. The Father as the originator within the Trinity is the giver of gifts including the Son and the giving of the Spirit, so it is naturally that the normal pattern is to pray to The Father whom we seek help and aid. But although this is the more common pattern the scripture does refer to Jesus as simply 'God' and so we could also pray to the Lord Jesus and say 'God' if we want, it just probably does not happen frequently because when we think of the Son we think of Him as the incarnate God and so we also think of him as a man also.
As the Son is God the scripture sometimes directly uses the term directly to the Son:
In Titus we see the terms used as synonyms. First God as the Father, then God as the Son:
Calling Jesus the "son of God" implies that he is God. This may not be a persuasive argument if it were not for Jesus being the only-begotten son of God. Angels, although sons of God, are not begotten. Christians, although sons of God, are begotten via regeneration, not generation. Only Jesus, the only-begotten son of God, is begotten via generation. He shares the same nature as his Father. His Father is God; therefore, he is God. I am human because my father is human.
Again, Jesus is the "only-begotten son of God." That means that he is the same nature as his father, and his father just so happens to be God Almighty. This means that Jesus is also God Almighty. Hence, in the Athansian Creed, it is written, "Deus est ex substantia Patris ante saecula genitus," that is, "He is God, from the substance of the Father, begotten before the worlds..."
In Oration XXIX, Gregory Nazianzen wrote,
Trinitarian Christians most often refer to Jesus by name or by the title of "The Son of God" to distinguish between the Three Persons of the Godhead. (The title of "The Son of Man" is a specific reference to a prophecy in Ezekiel with which Jesus identifies Himself.)
The Doctrine of the Trinity can be explained as such:
Jesus had a specific role in that He is the One who became a man. Neither the Father nor the Spirit did so. So, we often reference Jesus specifically because of His role in redemption.
However, we may refer to Jesus as God and be correct in doing so. Indeed, we often say the "God became a Man," and we mean by this that The Son of God became a Man--not the entire Trinity.
So, to answer your question, we don't refer to Him as God all the time, because we are identifying and distinguishing Him for His Incarnation, Vicarious Sacrifice, and Resurrection. Yet, we can and do refer to Him as God at times--just not as often as we refer to Him by His Name or His titles.
See this question for more information on the Biblical Basis for the Trinity.