undef $/;
open(IN, "d:\\xyz.txt")	||	die "Cannot Open file\n";
$str = <IN>;
$str =~ s#<index-entry id=".*?"><index-heading></index-heading>\n</index-entry>##gsi;
print $str;


Input :
<index-entry id="idx-12427">
<index-heading>Zone of proximal development</index-heading><intra-ref refid="00067.p0040" locator-type="pii" locator="B0126574103000672"><b>3</b>47</intra-ref>
<index-entry id="idx-12428"><index-heading>definition</index-heading><intra-ref refid="00067.g0040" locator-type="pii" locator="B0126574103000672"><b>3</b>45</intra-ref>
</index-entry>
</index-entry>
<index-entry id="idx-12429"><index-heading></index-heading>
</index-entry>
</index>