SET      --- STREAM OPEN TYPE           =      r
     SET      --- STREAM READ LENGTH         =
     GOSUB    --- STREAM OPEN
     SET      --- STREAM EOR SEQUENCE        =      LF
     IF       --- STREAM RETURN CODE         NE     0
     *
     *        read tab file record
     LABEL    :NEXT RECORD
     TRAP
     GOSUB    --- STREAM READ
     IF       --- STREAM RETURN CODE         EQ     0
     IF       --- STREAM BUFFER              EQ
     GOTO     :NEXT RECORD 

The field --- STREAM READ LENGTH is used for two things. If set to a value other than zero the READ subroutine will limit the data bytes it reads to no more than that many bytes. What gets you is that your READ routine also uses that field to tell you how many bytes it actually did read. So, the first time you call it the value was zero, it read in number of bytes (if you count the tab bytes) up to the linefeed and set that number of bytes into this field. Since you didn't reset it to zero that value carried forward to the next read. It read that number of bytes and stopped leaving the rest<lf> unread. The next time you called read it read the remaining number of bytes up to the linefeed and set the length to that number. And so on.....
So, you need to set this field to zero before each read attempt.