The DHS published a notice in October 2014 advising DACA recipients that they could file their request for extension up to 150 days (5 months) prior to expiration. As with all things government, very few of the DACA recipients, who tend not to frequent government websites, knew about the memo and many did not file so far before expiration perhaps thinking that extending a work permit was a like extending a drivers license, its is done in a few minutes. As an experienced immigration lawyer will tell you, the USCIS does nothing quickly, and certainly does not worry that a person may lose their job or their driver's license just because they cannot efficiently print a new card after a background check.
Perhaps responding to the increasing number of panicked calls to their service centers (and from immigration lawyers), USCIS issued another memo in January 2015 advising DACA beneficiaries to file in the window between 150 and 120 days prior to expiration. USCIS also said that if the exension is pending more than 105 days, they can contact the USCIS online with a request for a status:
USCIS’ current goal is to process DACA renewal requests within 120 days. However, you may submit an inquiry about the status of your renewal request after it has been pending more than 105 days. To submit an inquiry, please visit egov.uscis.gov/e-request or call the National Customer Service Center at 1-800-375-5283 (TDD for the hearing impaired: 1-800-767-1833)If your DACA renewal case has been pending for at least 105 days, we strongly encourage you to actively follow up with the USCIS directly at the website and phone number provided.
As to the first question? Why is it taking so long to renew a DACA work permit after the applicant has paid $465 and taken their fingerprints? The crushing number of cases? Hardly. Extensive background checks? Not likely. Bureaucratic intransigence and poor management of resources? That sounds like a more likely answer. Like all things with USCIS, getting answers takes time, but when that time directly impacts a person's ability to work and drive, it is time to get aggressive.
USCIS has uniformly refused to abide by a time in which it MUST issue these work permits (if all other criteria are met). So the only solution for DACA recipients facing this type of problem is to call USCIS, and to also call their congressman or senator. Each of those offices have individuals whose job it is to inquire on behalf of constituents (including DACA recipients) as to why your case is taking longer than normal. Be aggressive in seeking a response to your application. You paid for "customer service," you deserve to get actual timely service.