AOL Passwords hacked from iPhone

Question

I have had my AOL account for close to 15 years (since it's inception really).  I've had a few problems wiht my password being hacked over the years, but nothing like what I'm going through now.  I rarely check my email through their website - I use my iPhone 4S. 
It all started when I was going through my AOL spam folder on my iPhone looking for a legitimate email from my lawyer.  When I moved that message, it opened the next message (truly spam) that contained a link (and possibly an attachment...I don't remember).  I NEVER open junk email on my phone, I usually just delete it.  Next thing I know, my AOL account is sending rogue emails to every address I've got stored in my phone.  It all happened in a 6 hour span.  I changed my password, and updated it on my phone and thought all was good.  Then I received an email from a friend that looked legit so I opened it.  As soon as I did it, I knew it was a mistake, so the cycle started again.  I've change my password at least three times since the second time and have used a random combination of letters (mix of upper and lower case), numbers and symbols 12 characters long, so I know it's not easy to hack, I keep having this problem daily unless I remove the account from my phone - in which case, everything is fine...the problem only seems to be present when I set up my account on my phone.
It seems like there's a keylogger or virus on my iPhone 4s.  I've updated my OS, I've updated my computer, I've backed up my iPhone...what else can I do?  Should I replace my iPhone, or delete my AOL account permanently and change to gmail?  HELP!!  I'm at my wits end and my friends are tired of getting strange emails from me! 

Answer 1

verything seems fine after the password is changed until the account is added to Mail app on my iPhone.  Then within anywhere from 3-10 hours afterwards, I get all this returned mail.
I can't say what's going on there without getting my hands on your stuff and doing tests, which obviously isn't possible. However, I can tell you for sure that there's no way this is malware, unless your phone is jailbroken.
Jailbreaking is hacking your phone to allow it to run apps that didn't come from the App Store. If you did that, you removed all security from the phone, and it's possible you could be infected with something.
One thing to think about... has anyone untrusted had unsupervised physical access to your phone? It's possible that it could have been hacked under such conditions (physical access is required), and some kind of keylogging software installed.
In all, it would require some very specific circumstances for your phone to be the problem.
I've pretty much decided to just close the account since that seems like the next logical move.
That's probably what I would do. AOL has been struggling to maintain relevance in a post-modem world, and they're not doing a very good job of it. I used to be an advocate of AOL "back in the day," when expectations were different, but I ditched AOL a long time ago. They just stopped being able to do what I needed to do.
If you want to stick it out with AOL a little longer, when was the last time you tried changing your password? It would not surprise me at all if their servers were affected by the Heartbleed bug, and if they were a bit slow to fix it. (I would hope they've fixed it by now, but you never know, and most companies are being oddly close-mouthed about this.)