I would prefer a two step approach avoiding look(ahead|behind|around) assertions: first find patterns like a repeat of letter followed by a dot, then remove the dots and replace the pattern. Like this:

use strict;
use warnings;

my $str = "a history of u.s. coast guard aviation.  M.C. Esher";
$str =~ s/\W\K((\w\.)+)/ $1 =~ s{\.}{}gr /ge;
print "$str\n";
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The \W\K at the beginning is required to avoid matching "am.c.". It will also match a single occurence of letter followed by dot but that can be easily fixed by requiring two or more repetitions.

Update: removed the unnecessary non-capturing ?: from the regex.