If the next wave button that sends the wave can’t be pressed it’s because you’re clicking on a badge that shows there is a button outside the screen.
Kingdom Rush Vengeance levels are all widescreen and if your screen is not wide enough to fit it you can always pan the level by clicking over the background and dragging to the sides, like this.
NOTE: We changed this in version 1.9.9.19 and the badges can now be clicked, and the screen will pan to show you the actual wave button.