My initial license took a full three months to come through, in Macomb Country where you actually have to go before the board. Did my CPL class and paperwork in October of last year and didn't get the court date and license until January 11th.
Don't worry they'll make it up to you upon renewal.
No worries on the renewal though. As long as you get your renewal paperwork complete and submitted (and paid for up front) 61 days before it expires, then you have no worries of a lapse. [I have to cite that, right?]
28.425l License; validity; duration; renewal; waiver of educational requirements; fingerprints.
Sec. 5l. (1) A license to carry a concealed pistol issued on or after July 1, 2003 but before July 1, 2006 is
valid for 5 years.
(2) A license to carry a concealed pistol issued or renewed on or after July 1, 2006 is valid until the
applicant's date of birth that falls not less than 4 years or more than 5 years after the license is issued or
renewed, as applicable. Except as provided in subsections (7) and (8), a renewal of a license under section 5b
shall, except as provided in this section, be issued in the same manner as an original license issued under
section 5b.
(3) The concealed weapon licensing board shall issue or deny issuance of a renewal license within 60 days
after the application for renewal is properly submitted. The county clerk shall issue the applicant a receipt for
his or her renewal application at the time the application is submitted. The receipt shall contain all of the
following:
(a) The name of the applicant.
(b) The date and time the receipt is issued.
(c) The amount paid.
(d) A statement that the receipt is for a license renewal.
(e) A statement of whether the applicant qualifies for an extension under subsection (4).
(f) The name of the county in which the receipt is issued.
(g) An impression of the county seal.
(4) If the concealed weapon licensing board fails to deny or issue a renewal license to the person within 60
days as required under subsection (3), the expiration date of the current license is extended by 180 days or
until the renewal license is issued, whichever occurs first. This subsection does not apply unless the person
pays the renewal fee at the time the renewal application is submitted and the person has submitted a receipt
from a police agency that confirms that a background check has been requested by the applicant.
[There's more. Look up the law for complete details on a renewal extension if that situation ever applies to you.]