It might be because key() selects only nodes in the document containing
the context node, which you've made into the stylesheet itself with your
xsl:for-each.  So there are no nodes matching /items/item to be selected.

I'm guessing that you are stuck using XSLT 1.0, because you don't need to
do the document('') shenanigans in XSLT 2.0, so the latter's
three-argument version of key() likely won't help.

above-quoted xsl:apply-templates in another xsl:for-each that puts the
context node back to the document that you want to process:

<xsl:variable name="item-document" select="/"/>
<xsl:for-each select="document('')//me:month">
  ...
  <xsl:for-each select="$item-document">
    <xsl:apply-templates select="key('by-month', $month)">
    ...
  </xsl:for-each>
</xsl:for-each>

but it's starting to look a tad messy.

Cheers,
Adam.