Is it possible to make anaerobic media too reducing?
I notice that you don't specify pH, which might be important.

I don't know if you can put in too much reducing agent (I suspect not), but a large excess is often required as the equilibrium constants for disulfide exchange reactions are typically close to unity (see Cleland, 1963). 

I also don't know if any of following has any relevant to your problem (again, I suspect not), but I want to briefly comment on two aspects of using thiols to as reducing agents in general.

Firstly, the oxidized (disulfide) form of thiols may react with a protein sulfhydryl. Using &beta;-mercaptoethanol as an example (Scopes, 1993, p 320), something like the following may occur, where the reducing agent becomes (reversibly) bound to protein. If the reactive sulfhydryl is at an enzyme active site, this may lead to inactivation.  

$$\ce{2 HSCH2-CH2OH  +  O2 -&gt; HOCH2CH2-S-S-CH2CH2OH + H2O2\tag{1}}$$

$$\ce{HOCH2CH2-S-S-CH2CH2OH + HS-{Protein} &lt;=&gt;HSCH2-CH2OH + HOCH2CH2-S-S-{Protein}  \tag{2}}$$

As stated, equilibrium constants for thiol exchange reactions are often close to unity (Cleland, 1963).,
 $$\ce{R1-S-S-R2 + R3-SH &lt;=&gt; R1-S-S-R3 + R2-SH \tag{3}}$$
  For this reason, many protein chemists prefer to use dithiol analogs of threitol (dithiothreitol, DTT, or Cleland's reagent) or erythritol as reducing agent, as the oxidized form of these compounds are cyclic disulfides, where the equilibrium constant is displaced to the right  (see Cleland, 1963). 

There is also the question of stability. 

The half-life of thiols in solution are markedly pH and temperature dependent, as the  table below shows. The half-life of &beta;-mercaptoethanol at pH 6.5 and 20&#8451; is greater than 100 hours, but at pH 8.5  and 20&#8451; it is only 4 hours. 

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The above table was taken from  Stevens, R, Stevens, L &amp; Price, N.C (1983) The stabilities of various thiol compounds used in protein purifications, published in (the now-defunct) Biochemical Education. The full article is freely available as a pdf from the Wiley website