Translation of RNA into proteins
In the basic model of protein synthesis the events involving tRNA and amino acids are as follows (see any standard text, e.g. Lodish et al. section 4.4):


An amino acid is attached to the appropriate tRNA (the one with the anticodon that recognizes a codon for that amino acid) by one of twenty specific amino acyltRNA synthase enzymes in a reaction requiring ATP. This is called charging or aminoacylation of tRNA.
The tRNA corresponding to the mRNA codon is brought to the ribosome by an elongation factor (EF1) and the peptidyl transferase activity of the large ribosomal subunit catalyses the formation of a peptide bond between the growing polypeptide chain* and the amino acid of the tRNA, releasing deacylated tRNA.


I am unclear why you are concerned with this problem, but if there were two alanine codons in the mRNA, in theory after a particular discrete tRNA molecule had inserted the first alanine it could be recharged by the aminoacyl tRNA synthetase and then be used to insert the second alanine. However the concentration of tRNA molecules in the cell needed to support protein synthesis is such that the actual probability of this same discrete molecule being used, rather than another tRNA carrying alanine, is remote. 

*A real-life complication is that a polypeptide chain has to be initiated by an initiator methionine-tRNA that is distinct from the methionine-tRNA that inserts internal methionines (see Lewin et al. section 4.5).