Bench Supply Amps - 4AA Batteries
I found this note on size AA batteries at this website blog. It is a large blog that clears the air about amps vs. amp/hour ratings. Based on this blog I would limit current to 500 mA. Though a Alkaline battery might be rated for 2000 to 3000 mAh, that could be a overload value and not the nominal current drain expected by the battery manufacture.

Speaking in general terms, you could expect the battery to run for about 10 hours at 10% of its mAh rating, but not all battery types follow such a drain curve, and not all loads react to a low battery the same way. Please read the blog.


  Pololu Blog » Engage Your Brain » Understanding battery capacity: Ah
  is not A Posted by Jan on 12 November 2010
  
  AA batteries. A typical alkaline or NiMH battery in the standard “AA”
  size has about 2000 to 3000 mAh (or 2 to 3 Ah). With a cell voltage of
  1.2 V to 1.5V, this corresponds to 2 to 4 Wh per cell.