What is the mental state called when I forget my thoughts?
Suppose I am talking to someone and while talking more thoughts come to my mind that I wish to talk about. I postpone those thoughts, however, to tell everything synchronously, i.e., I wish to tell the old thoughts first and then the new thoughts in sequence. But by the time I finish telling previous thoughts and try to come to those new thoughts that I postponed to tell, some are vanished. This must be a very common phenomenon, as everyone has experienced the dreaded
What on earth was I about to say...?
What is the term for this mental state, or of the process mentioned?
I believe you are describing the difference between long term and short term memory. Our brains can only remember about 7 pieces of new or random information all at one time. Brains store information in short term memory for about 5-10 sec then it is either fogotten or it goes through the more complicated process of being coded as a long term memory that is more permanent.