I think the lost neutral diagnosis is accurate and more than likely the culprit.
Here is what I would do, but ONLY if you are confident that you won't kill yourself trying to do this. If you are not comfortable working with AC (and potential death) hire a licensed electrician to do this. Observe all safety precautions: identify and turn off the breaker for the receptacles you are working on (another plus for this is that if you do not have a properly labeled service entrance you can do so when you are doing the work); wear insulated sole shoes; wearing thin workman's gloves is a good idea: be vewwy, vewwy caweful at all times.
The process is simple - remove each receptacle, check the wires for discoloration, clean the wires and tighten the snot out of each connection. Pay special attention to the discoloration of the wires. A lot of black corrosion means that the wiring was not well tightened. If you have red corrosion you probably live around salt water and should check them more often. If you live in a humid area putting a thin coating of No-ox-id A special
http://www.sanchem.com/aSpecialE.html or equivalent will prevent most of your problems in the future. It is electrically conductive and need to be applied very sparingly. Do NOT use tail lamp grease - that suff is bad ju-ju over the long run. After you have cleaned up and tightened everything re-install the receptacle and move on. IF any screw feels even the least bit that it is stripped, move the wire to the adjacent pole, or better yet, replace that receptacle. This is a PITA, but will probably cure your ills.
I recommend that you leave the service entrance to an electrician unless you absolutely know what you are doing and feel confident work around 240V that can dump 200A before you can even think Always - Safety first.
You never mentioned where you live. If you live in a cold climate, this could be part of the problem, too differential heating between winter and summer can loosen screw more readily. I check receptacles once a year for tightness.
REMEMBER: SAFETY FIRST. We don't want to call you Sparky.
While you are at it replace the receptacles that feed your system with some really good ones. There are a bunch of audiophile (I hate that term) recommended ones available. I happen to know where you can get some good cryoed ones for not a lot of $$$
Check back after you have done all of this and let us know the results. This should cure the problem. If not, we'll figure something else out.
Dave