Regular expression parsing has some unfortunate corner cases that can eat up a lot of processing cycles (see http://www.regular-expressions.info/catastrophic.html). The regular expression state machines can also eat up a lot of memory. Because of this, BigQuery has a budget for regular expressions. The current value is something like 2MB per query. This is a guideline, not a published guarantee, however, and is subject to change at any time.
BigQuery is documented to use Re2 (code here: https://code.google.com/p/re2/) for regular expression parsing; You can try running your regular expressions with this library using a budget of 2MB and check whether they succeed or not.