Can a lack of oxygen cause septic tank deterioration?
There are several forms of acidic (sulpheric mainly) conditions causing concrete to decompose, external and internal.

External acid can be caused by sulpher in the ground water.  

Anaerobic bacteria can indeed cause hydrogen sulphide gas which then can cause sulpheric acid.
High levels can quickly destroy a septic tank.

Aeration of the sludge effluent changes the chemistry to aerobic bacteria and stops the formation of HS gas.  

Update
The phenomenon of HS gas formation leading to concrete deterioration is known as Crown Rot.  Anecdotally, this has been linked to several sources.  High vegetable matter (from garbage disposer use) and high levels of sulpher in well water.  Active venting does seem provide benefits in reducing the HS gas. (thanks to Capt. P).