In order for pos to remain set, you need to use the /g modifier on the regex. This is why the snippet with the while loop works. So, just use /g without the while loop:

$_ = "abcdmefg";
if ($_ =~ /m/g) {
  print "matched 'm' at ",pos,"\n";
}
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However, if you're just looking for fixed substrings, you may prefer to use index instead:

$_ = "abcdmefg";
if (($pos = index($_, 'm')) >= 0) {
  print "found 'm' at ", $pos, "\n";
}
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Keep in mind that pos returns the location where the previous match ended, while index returns the location where the substring begins. Thus, these two snippets give 5 and 4 respectively.