Correct. Under Ohio law - ORC 2923.125 (D)(1) - the sheriff's office has 45 days to either issue the license or deny for cause in writing (and, since not otherwise specified, those are *calendar* days).
Unfortunately, when you are able to contact them, you really don't have many options. I'd start with mentioning the 45-day specification under the law, and noting that there are *no exceptions*, like for the background check being delayed (which is what I expect their excuse will be), etc. If that is their excuse, you might also explain that if something does come back in the background check, they can always revoke the license. Then, tell them that you are coming to pick up your license. If they tell you that you can't, one option would be to ask to speak to the actual County Sheriff so you can discuss with him how his staff is not in compliance with Ohio law. Or, ask to be transferred to the clerk of courts so you can file a writ of mandamus to compel them to fulfill their duties under the law. (This might *really* get their attention - nobody in government wants to have a judge rule against them like that...)