Do you have the original iPad mini or an iPad mini with Retina Display?
The iPad mini with Retina Display is slightly thicker and it made a difference for me. I originally tried the RAM part number (RAM-HOL-AP14U) that Marauder listed and not only was it tight, it peeled up the corners of my screen protector trying to insert it. That's when I found out there is a specific holder for the iPad mini with Retina Display, it is RAM-HOL-AP14R (the 'R' is for 'Retina'). I swapped out the holder for the correct one and it made a BIG difference. Keep in mind this RAM holder requires the iPad mini to be inserted without a case/cover.