Why would a candle require a much larger wick than normal for its size? I was recently given a couple of fairly large beeswax pillar candles by a friend who got them from his church.  They were going to be thrown away, but he knew that I dabble in candle making so he salvaged them.  They are beeswax, so well worth salvaging, in my humble opinion.

The reason they were being thrown away is that they were tunneling very badly.  As is well explained on the web, that's usually a result of being underwicked.  

I have a couple of votive molds, so I used them to make a few candles from wax taken from the big pillars, and then consulted this page to find that something in the range of an HTP 31 through 52 should be about right.

So I tried an HTP 41, and it also burned extremely underwicked.  Cutting a long story short, I kept increasing the wick size till I got a satisfactory burn, and found that I had to use an HTP 126 to do so.

That's simply a huge wick for a standard votive, it's more appropriate for a 3" to 4" container.  Yet it is somewhat consistent, you'd think that a commercial company would know the correct size wick to put in a candle, and yet that burned like it was underwicked, exactly like the HTP 41 I tried.

So, is it possible that the beeswax is somehow altered, or degraded or something that causes it to require a much larger wick to burn correctly?

As noted earlier, I dabble in candle making, but I'm no expert.  Thus the reason I'm asking.  I usually consult a wick sizing page like the one I linked, and use their advice to find a good starting size.
Most of the time, I get a good burn within a size or two of where I start, just not in this particular case.
The problem could be the composition of the wax.  Could there possibly be a certain percent of soy wax in the pillars, in addition to the beeswax?  The Wick Guide that you referenced states:


  Higher viscous waxes such as single pour paraffin wax, soy (vegetable) wax, and beeswax, may require (wicks) up to several sizes larger than the recommendations below.


Here is another source that discusses how soy wax can cause problems such as tunneling:


  Tunneling occurs when the wick used is too small and flame does not sufficiently melt the whole surface of the candle. This will result in the candle burning unevenly, a smaller flame, lower scent throw and the candle extinguishing itself.  The best candle tunneling fix is to use a larger wick size...