How to fix it. (You will need # 0 or 1 Phillips screwdriver, magnifying glass. sharp knife point or Xacto knife point for scraping.)
1. Remove the screws and take the back off the speaker.
2. Squeeze and Disconnect the tweeter from the little "motherboard". (just for easier access to the underside.)
3. Examine the underside of the motherboard, especially the two terminals that mate with the tweeter connector.
4. There you will encounter one of two problems either a.) a cold solder joint on one or both of the pins (less likely)
or - (more likely) a stupid thread of solder "bridging" across the two circuit board traces - which are stupidly closer together than they have any reason to be.
5. Take something sharp - knife blade point - and make a few scrapes between the traces - BE CAREFUL NOT TO OVERSCRAPE AND CUT OTHER TRACES ON THE LITTLE BOARD. YOU JUST WANT TO CLEAN BETWEEN THE PINS.
6. If this doesn't fix it, you probably have a cold solder joint.. Touching it up with a spot of heat from a small soldering iron should cure the problem. You should be able to "see" a cold solder joint - which often looks "granular", not glossy - or wiggle it loose.
But 90% odds would favor the bridging fleck of solder between the pins.
7. Reconnect the tweeter to the motherboard with a good firm scrubbing action. Reassemble the caase - and you should be good to go.
All problems s/b this easy - and unsolved where the tweeter cuts in and out is MADDENING know.