The sound from the main unit speakers fades away after a few seconds but the bass speaker continues to work

If you are talking about the driver cones in each of the units, then it's odd that they should have gone, unless they have driven too hard or damaged (say by a child poking them). Double unit speakers have a crossover built into that separates the sound into treble and midrange or bass.
If the sound coming out is "treble" the high frequency that shows the bass units are not working.
Make certain all the wiring is good to the speakers and if you can see the bass speaker check it is not damaged.
If you need to, go inside the units and connect a 1.5 battery across each speaker terminal for a second. If it "pops" then it's working.

Could be interference from another electrical device or a loose connection. Or you forgot that you were watching Saving Private Ryan.

Turn off the movie, and then try moving them away from anything electrical; TV, monitor, PC mainly. Cordless phones can do it as well.

Swap the speakers left-to-right to isolate if it's an amp or speaker problem. You have not indicated this was done.

I don't believe this hookup is amplified; but, if you have used the regular unfiltered speaker connections from your receiver/amplifier to hookup the subwoofer, the system will pass the signal thru the outputs subject to the crossover adjustment on the back panel. You cannot get the full signal if your system is sending only the bass signal to the subwoofer. I have copied the instructions below from the manual. You would set the high freq crossover to the low end of your satellite's frequency range. The full manual is here: http://www.jbl.com/EN-US/Products/Pages/ProductSupportDetails.aspx?PID=PSW-D110

High-Pass Control
• If you hooked up your subwoofer
as shown in Hookup
3 on page 4, you also have
the capability of adjusting
the high-pass frequency.
The High-Pass control
determines the frequency at
which the main speakers
will start reproducing
sounds. If your main speakers
can comfortably reproduce
some low-frequency
sounds, also set this control
to a lower frequency
setting, between 50Hz –
100Hz. This will concentrate
the subwoofer’s
efforts to the ultradeep
bass sounds, while your
main speakers continue to
reproduce the mid-bass
information. If you are
using smaller bookshelf
speakers that do not extend
to the lower bass frequencies,
set the high-pass crossover
control to a higher setting,
between 125Hz – 180Hz.
With this setting, your main
speakers will not have the
burden of reproducing any
low-frequency sounds.
• If you hooked up your subwoofer
as shown in Hookup
1 on page 3, the high-pass
frequency is fixed at 180Hz.
• If you hooked up your subwoofer
as shown in Hookup
2 on page 4, there is no
high-pass control. Unless
your receiver/amplifier
incorporates a high-pass
crossover, your main speakers
will continue to get a
full-range signal.
Final adjustment and blending
of the low-pass and high-pass
controls may evolve over several
listening sessions. A good
starting point would be to set
both the low- and high-pass
controls to the same frequency
and adjust from that point.

Hello Adam Hi, it looks like your main IC amplifier inside the main bass box is bad, need to replace that IC. What are your plans, do you want to do the repair or have it service by a tech guy.

You can buy aftermarket crossovers that will reduce or eliminate bass frequencies to some or individual speakers. They are wired in line with the speakers in question, ususally right before the speaker itself and tucked away inside the door.

POSSIBLY A BREAK IN THE SPEAKER SUPPLY LEADS TO THE ACTUAL BASE UNIT
WE HAD THIS AND IT WAS NOT THE SPEAKER BUT THE BOLT ON CONNECTION UNDER THE SPADE TERMINAL ON THE BACK OF THE BASS UNIT

You need to take apart tthe sub woofer and check the connection to bass speaker for continuity. It sounds like an internal broken connection to speaker on sub woofer unit.

Have the speaker checked out and if it checks good you need to take the amp back to the repair center and have them test it better. Most repair centers have a 30 day warranty on the work they perform. Make sure they know what the problem is in detail, so they know how to check it properly. But my first thought is the speaker could be faulty. You can check the speaker yourself by switching them at the amplifier. If the same speaker sounds bad you know it is the speaker that is bad. If the sound is bad from the other speaker, then the amp is bad unless it is coming from the head unit. You can also switch the RCA input jacks after that and see if the problem changes speakers, if so, the RCA output of the head unit is bad, but that is less likely.

You need to go into the setup menu and find out if the radio has a sub low-pass filter that redirects the bass to the pre-out for the subs, and away from the main speakers. Fiddle in the audio menu.