Why, in "Through the Tunnel," does the boy consistently mention his mother's naked arm?Just out of curiosity because as I was reading this story...

What an interesting question!  Given what we know about
Jerry's mother, we can use this information to help construct a character analysis of
her. 

At the very beginning of the story, Jerry's mother's
naked arm is described as being "very white in the sun."  The next day, Jerry observes
her "bare arm, now slightly reddened form yesterday's sun."  Primarily, nakedness (as
used in this context) suggests vulnerability.  Further, readers might also
consider Jerry's mother's slight sunburn to be representative of a sort of weakness or
vulnerability.  Both suggestions seem to be consistent with other examples of
characterization we can find for her. 

As the story opens,
readers are aware that Jerry's mother is a widow who worries and second-guesses herself
frequently.  She obsesses over whether or not her decision-making is beneficial for her
son and whether her parenting has been effective.  All of these qualities, on some
level, suggest weakness or vulnerability.  When Jerry's mother first (and briefly) loses
track of her son, she is impatient:

readability="8">

She frowned, conscientiously worrying over what
amusements he might secretly be longing for, which she had been too busy or too careless
to imagine. 

Then, when Jerry
expresses a desire to venture down to the bay, his
mother worries:

readability="6">

She was thinking.  Of course he's old enough to
be safe without me.  Have I been keeping him too close?  He mustn't feel he ought to be
with me. I must be
careful.

Again, her
vulnerability to the sun might suggest a vulnerability in her character.  Further
evidence to support this idea can be found at the end of the story, after Jerry has
successfully conquered the tunnel and his mother questions him about his
day:

"Have a
nice morning?" she asked, laying her hand on his warm brown shoulder a
moment.

Here, Lessing creates
the image of strength through her description of Jerry's shoulder by using the word
"warm," as the shoulder is typically an indicator of physical strength (which Jerry
needed to be able to accomplish his goal).  However, in the next sentence, she observes,
"You look a bit pale," which suggests weakness and contrasts Lessing's previous
description of Jerry's coloring. 

Again, great question. 
I'm not sure that there's a "right" answer, but as authors consciously include details
like the references to Jerry's mother's arm, this is my best guess. Hope it
helps!