What county in MO are you in? I got mine through St. Louis County and it took maybe 2 weeks, but there are a few counties out there I have heard will push that 45 days to the max and some even go over (although not legal, nobody does anything to stop it).
I think the vast majority of MO counties are getting permits issued very quickly though. You may want to consider joining this board for all of your Missouri CCW questions: http://www.missouricarry.com/forums/
Very nice folks over there who can probably give you more detailed information county by county. Stop by and say hi, I'm "Monkeyhouse" over there.