Keep getting "your Apple ID or password is incorrect" message

I have one iTunes account that I have linked all my kids' iPods to - so I can control purchases, etc. The kids know that I am the keeper of the keys when it comes to purchases - I don't let them have the password, and only enter it when they can't see. Relevant, because they're not trying to gain access to itunes, etc.

About every 4-6 weeks, when an app needs an update, the ipods all start displaying the error message ""your Apple ID or password is incorrect".

I enter the password at Apple.com - works fine.

I enter the password through iTunes - works fine.

I enter the password on the ipod - get the 'incorrect' message.

I have to go through the routine of signing out of iCloud, deleting the account from the devices, resetting my main apple ID password MULTIPLE TIMES, and sometimes even doing a hard reset on the ipods. Occasionally, when I try to sign out of the iCloud, it will tell me that my password is invalid, and that I have to go through the reset process...AGAIN. So, I follow the icloud reset password, then get prompted to 'update your password in settings' - where I update it and promptly get ANOTHER error message telling me my password is incorrect and must be reset....

Eventually (usually after I have changed my main apple password 4 times or so), the ipods will update.I log to itunes, and verify the password works. I log into iCloud with the same password, and verify it works.

I have tried this in one sitting - repeatedly changing the password until they are 'taken' by the system.

I have tried this over the course of a few days - changing the password, verifying it works, then waiting a day before trying any other steps.

In both cases, it seems that multiple attempts are needed for the passwords to effectively change. And by multiple, I mean MORE THAN 10.

Long story, but I have two concerns:

1. Why - when I explicitly change my itunes pw to match my icloud pw, does it eventually 'fail' telling me that it's incorrect? This occurs about every 30-60 days, and I end up spending the better part of an evening mashing various password after password into the system until it decides to 'take'. Once I get them changed and in sync, I can access iTunes, iCloud, etc. - with NO ISSUES for about 30-60 days. Then the Cycle of **** begins again.

2. Is there a simple way to avoid all this? I'd rather not have iCloud or any of this if I have to put up with the repeated hassle of an evening of choosing passwords that I HAVEN'T used in the last year...and given that I go through about 10-15 pws when it acts up (as well as multiple hours of frustration), it's a struggle. If it's due to a security issue, shouldn't I get some sort of notification? I certainly get emails when Apple wants me to buy something.....