It depends on where you live. Here in Mass, our police chiefs have "discretionary" authority, which means they can deny "just because". And yes, our FLRB HAS overturned their denials that were not supported by anything within the actual laws.
However, having an FID doesn't automatically qualify you for an LTC, as the requirements are more lenient fir FIDs.
If you are denied, the best thing to do is find out why. Your police chief (or licensing official) should be informing you as to why you were denied. If they don't, ask them. If they refuse to tell you, get a lawyer (preferably one that knows your state's gun laws).
I haven't been denied, but my renewal was held up due to a civil "warrant" (my car insurance defaulted, and car was impounded, when I was in Iraq... insurance said I owed them five dollars, the ADA and judge agreed to toss it due to the fact that I was in Iraq at the time, and had half my unit in the courtroom with me).