A fully grown organism is subject to senescence and on a narrow perspective one of the signs of aging is the accumulation of large amount of lipofuschin.
In unstressed situations protein homeostasis is balanced by folding and stabilization of proteins by chaperones of the Hsp family  and the controlled degradation of proteins by the proteasomal system.[source1]
One of the highlights of postmitotic aging is the intracellular accumulation of highly oxidized and cross-linked proteins, known as lipofuscin. Lipofuscin is insoluble and not degradable by lysosomal enzymes or the proteasomal system, which is responsible for the recognition and degradation of misfolded and oxidatively damaged proteins. These aggregates have been found in various cell types, including heart, liver, kidney, neuronal tissue, and dermal tissue, and are associated with the life span of a single postmitotic cell and, consequently, of the whole organism. Lipofuscin formation appears to depend on the rate of oxidative damage to proteins, the functionality of mitochondrial repair systems, the proteasomal system, and the functionality and effectiveness of the lysosomes. This review highlights the current knowledge of the formation, distribution, and effects of lipofuscin in mammalian cells.[source]
Lipofuschin is known to contain oxidised proteins,lipids and glycosides as follows:
This accumulation of aggregates is the final fate of protein damage under stress conditions. Under such circumstances oxidized proteins may not undergo appropriate proteolytic digestion but instead, cross-link with one another or form extensive hydrophobic bonds. It is believed that the cross-linked proteins react further with other cellular components, forming a fluorescent material referred to as lipofuscin (Fig. 1F). Lipofuscin is accepted to consist of oxidized proteins (30–70%) as well as lipids (20–50%)  and from the fifth decade of life, bound sugar residues were also detected in human lipofuscin. [source]
The lipofuschins are present in residual bodies of lysosomes ,the centre of protein recycling.
Lipofuschins render the non digestibility of the oxidised proteins as follows:
According to this model, an intralysosomal accumulation of lipofuscin can be considered as the long-term result of a decreased degradation of oxidized proteins and an increase in intracellular free radical formation. Metals, including Fe, Cu, Zn, Al, Mn, and Ca, comprise up to 2% of lipofuscin  and especially catalytic iron seems to be an important factor in further oxidation reactions of the initial protein aggregate. In mammalian cells iron is the most abundant cellular transition metal and a fundamental player in the above mentioned mitochondrial–lysosomal axis theory of aging [source]
Another major characteristic of lipofuscin is its ability to inhibit the degradation of oxidized proteins by competitively binding to proteolytic enzymes including the 20S proteasome as mentioned above as well as lysosomal proteases. How exactly the proteasomal substrate recognition functions is still under investigation, but one of the recognition motifs might be exposed hydrophobic patches from oxidatively damaged and partially unfolded proteins [5,28]. It seems likely that the proteasome also binds to such exposed hydrophobic oligopeptides on the lipofuscin surface but is then unable to completely degrade or to release these peptides, resulting in proteasomal inhibition [source]
The lipofuschins being the undigested remains,it can be said that the lysosome fails to recycle the entire endosomal protein specifically with aging (when it becomes very prominent).
Thus, some of the loss of amino acid may be attributed to its lack of recycling.