As tINY said, the most likely culprit is a rubbing voicecoil. It's also possible that you may have a cold solder joint or a bad coupling cap in the high-frequency amplifier.
You might try the following test:
Play a mix through a high pass filter. The Rokit G2 has a crossover frequency of 2400 Hz. Set your HP filter to 3kHz to eliminate most of the signal from the 5 inch LF driver and listen to the tweeter as you bring the level up and then down slowly. If you hear some low level sound (probably pretty distorted) and if the sound drops abruptly or becomes "buzzy" when you lower the volume slightly it's likely you have a rubbing voice coil.
However, if you hear nothing at all, and then if the tweeter begins to work well, and then continues to work well for a while after raising and then lowering the signal level, it's possible you have a HF amp issue like a cold solder joint, bad coupling cap or an internal connection issue.
If the speaker behaves like the latter situation, it may be worthwhile removing the back panel and visually inspecting the amplifier and internal connections. Be sure to unplug and disconnect the speaker completely before removing the amplifier panel.