When a device "pops" and immediately loses power that is a sign of an electrical short.
I.e., some situation is occurring wherein the electrical current is too much and the device's safety mechanisms, breaker or fuse, activate to shut off the device.
Why the electrical current is too much could be a faulty component within the device (speaker).
A capacitor being a component and may or may not be the cause per se.
You may or may not be able to test the capacitors yourself. And, likewise, you may or may not be able to make the repairs yourself.
Start by reading the following link regarding capacitors:
https://www.ifixit.com/Wiki/Troubleshhoting_logic_board_components
Then search for additional links more targeted to your situation.
And find a knowledgeable family member or friend to help you thereafter.
If you do the wrong thing(s) you may permanently damage the speakers.
So: 1) Gain some understanding of what is, or may be involved, and 2) Get help.
A pro to fix may be less expensive than new active stage speakers......