When is a regexp is not a Regular Expression?
tl;dr backrefs.

As soon as there is a \1 (or any number that isn't used to escape unicode) in the regexp it is not a regular expression. 

Backrefs allows you to match (a+)b\1 which matches n times a followed by b followed by n times a for any n>1. This is not a regular language (it's the poster child of a non regular language). 

It is necessary and nearly sufficient that the backref references a group that contains a regexp that matches an arbitrarily long string or that it contains a * or +. The only exception (that I found) of a regexp of the form (A)B\1 where A is a finite language (could be replaced by a enumeration of all words that accepts them). You can convert it to word1+Bword1|word2+Bword2 etc. because A is finite.

Look-around groups don't remove the regularness of the regexp. A(?=B)C is the cross-section of regexes AB.* and AC and the cross-section of 2 regular languages is regular. Negative lookahead is similar except using the complement of B.* (complements of regular languages being regular). Lookbehind is exactly the same as well A(?&lt;=B)C is the cross-section of AC and .*BC.