I've had this issue reported by a couple of users running my game on older laptops. They report that during moments when the game experiences frame loss, sometimes the button presses from the gamepad do not register.
This seems like a pretty serious issue as missed button presses are going to result in a lot of frustration for players. Thankfully, my game has no fail states, so the worst thing that happens in this case is that the player has to press the button again. But I imagine in certain game-types (i.e., action games), missing button presses would be a major problem.
When discussing this issue on Discord, Federico points out that gamepad input is polled, which is the cause of the issue.
For reference, this is where the issue was reported to me: steamcommunity.com/app/1526370/discussions/0/4407418033223539057