Can catecholamines degrade back into tyrosine, or, is synthesis irreversible? (in human body)
A glance at the relevant BioCyc entry tells us that each reaction in the catecholamine biosynthesis pathway is irreversible. The standard free energy change of each reaction—again from BioCyc—is given below. 

\begin{array} {|r|r|}
\hline
\text{Reaction} &amp; \Delta _r G' ^{\circ} \text{ in kcal mol}^{-1}\\
\hline
\text{Tyrosine hydroxylation} &amp; -93.0 \\
\hline
\text{Decarboxylation of DOPA} &amp; -3.09
\\
\hline
\text{Hydroxylation of dopamine} &amp; -67.9
\\
\hline
\text{Norepinephrine to epinephrine} &amp; -10.5
\\
\hline
\end{array}

Note that all the free energy changes are negative, i.e. all reactions are irreversible under physiologic circumstances. (For the last one, there is a simple explanation: S–adenosylmethionine is a powerful methylator [1].)

Another aspect is worth a mention. Under physiologic conditions, the reversibility of a reaction depends not only on the free energy changes involved, but also on what happens to the reactants and products. A large supply of reactants, or rapid removal of reaction products, can make the reaction physiologically irreversible. Applying this principle to the catecholamine biosynthesis pathway:


A steady supply of oxygen is available from the atmosphere—this drives the tyrosine and dopamine hydroxylation reactions in the forward direction.
The dihydrobiopterin produced by tyrosine hydroxylase is scavenged by reduction to tetrahydrobiopterin, which further takes part in the tyrosine hydroxylase reaction [1].
The carbon dioxide produced by DOPA decarboxylase is exhaled out.


This further adds to irreversibility.

Of course, as mentioned by @user1136 in the comments, it is theoretically possible to have a "reverse" pathway by coupling to ATP hydrolysis. However, I could not find any such pathway in database searches. 

Summary: To the best of my knowledge, humans cannot convert catecholamines back to tyrosine.



Reference


Nelson DL, Cox MM. Lehninger principles of biochemistry. 6th ed. New York: WH Freeman and Company; c2013. Chapter 18, Amino acid oxidation and the production of urea; p 695–730.