If you are unlucky, the magnet is falling off the back. I would take the woofer out and have a look. Changing the capacitors will certainly make a difference if they are dull. They should be crystal clear. If you are lucky, you have a loose connection. 

A loose connection, I agree.
Typically where the flex lead meets the coil copper wire. That will be on the outside of the cone
where you can see a solder joint covered in black, just where the flex lead comes through the cone
from the backside. Carefully scrape off the black paint to expose the solder joint and redo it.
Add a drop of glue, silicone or similar afterwards to avoid rattling.

Martin

I removed the woofer, to look at the connection, realised you ment the other "outside of the cone", put it back in and for now it works again... Won't touch it anymore  for the moment, but if the woofers fails again, I know what to do, thanks!