This leads me to thinks that it's not something inherent to the wearing of dress shirts and suits, but rather something specific to you, your particular clothing, and how you wear it.
Perhaps your shirt sleeves are slightly too short? Or might your suit coat sleeves be uncommonly snug? Does it happen with all suits, or just some? Or (and I ask this in a somewhat tongue-in-cheek manner) could you be OCD about the amount of cuff you show - I mean, do you feel compelled to adjust things if your cuff rides up 1/16 of an inch?
Perhaps a photo of you in your shirt and suit would prove helpful. In fact, two photos - one with your jacket off (so we can see how the shirt sleeves look), and a second photo of you wearing your suit jacket. Decent quality photos, if you please; it's frustrating when people ask for feedback on a photo, and the photo is of such poor quality that no real conclusions can be drawn.
In any event, please ignore anyone who suggests you resort to a stapler. Real men know that the "last resort" way to keep a shirt sleeve in place is with thumbtacks. Only the clueless bother with half-measures, such as staples. (And the less said about the duct tape crowd, the better.)