Bassman92 has probably hit it right on the head.
If the amps were faulty, the sound from the speakers would be more likely to be distorted than cut out.
Dry joints or loose connections inside the speakers can lead to one or both drive units cutting out.
If you are confident with opening up the speakers (the drive units are most probably screwed in from the front), take out the bass unit (this is the easy way into the speakers) and have a look at the wiring and crossover. Soldered joints can fail, either on interconnecting wiring within the speaker cabinet or on the crossover board.
When you have the speakers open, you could (very carefully) try moving the individual internal wires to see if the tweeter cuts out or comes back. Alternatively, do a bit of tapping around inside the speakers and on the drive units, making sure you don’t use any metallic object that could short your signal and damage your amp. If you find a dry joint, these don’t always look bad (think “hidden disabilities”). They could look ok from the outside but not be making a good connection inside the solder.
As I am not familiar with the Allaes, I don’t know if they have push-on connectors inside the cabinet, but if there are push-ons, try pushing them back into place or wiggling them to clean them.
If you have access to a multimeter, you could try measuring the drive unit impedances but this will be affected by the crossover.
This sort of problem should be soluble with a systematic approach.
Try the following:
- Swap the left speaker with the right, leaving the speaker wires where they are.
- Put the speakers back where they came from and try swapping over the speaker cables.
- Try different speakers with your existing amp
- Try your speakers with a different amp
If the problem moves around when trying any of the above, it will point the culprit out. My money is on the speakers.
Lots of the other contributors have offered sensible advice about whether to upgrade or not, but unless you sort out the problem with the speakers, you won’t be able to sell them for a decent price.
One last thing. When you sort out the speaker problem, check the directionality of your system interconnect cables and speaker cables. If they are Naim, they are directional and this will affect the sound. Speakers are easy, there are arrows that point from amp to speaker. For the interconnects, look at the manual. If the interconnect cables are unmarked, try turning them round one at a time. If the sound improves, leave them that way. It is also worth unplugging all your cables and plugging them back in to clean the surfaces. A bit of wiggling may also help with the cleaning.