I have had/ am having the same exact issue. I have used AOL for well over 25 years now. I recently reconfigured an older iMac which runs OS 10.6.8 and thus the Mail 4.6 program. I noticed immediately after doing a CLEAN install of the whole system on that computer that I could not access AOL using the Mail program (I could access it using Safari and going to AOL.com, no problem) so I knew I had the password right.
Strangely enough, using "connection doctor" it became clear that my SMTP (sending mail) server would connect...like lightning in fact. However the IMAP (incoming mail) server would not connect no matter what. You techies tell me why that would be. I'm assuming it's a glitch caused by AOL/Verizon's increased security or something that is more technical than Mail 4.6 can handle. So my IMAP server side of my AOL account was out and thus no mail was getting through.
After two days of trying to contact AOL customer service and twice, after long holds having the call dropped, I successfully contacted AOL service today. I talked to the first rep. Why my mail wouldn't work was over their head so they passed me on to a kind person in their tech department. I had to sign up for AOL's special technical support to get this, but the first 30 days were free and I could cancel, so why not? (make sure you ask for the free trial period, then you have nothing to lose when they finally tell you they can't help you ;-) )
My impressions of AOL support: First of all they don't seem to be too conversant with Apple equipment. Secondly after trying a number of things including using their specially generated password obtained from AOL security and failing, the tech consulted a higher authority tech who said that AOL no longer supports the software I'm using with OS 10.6.8 and Mail 4.6. One would think they'd have publicized that, unless they have some programmers trying to correct the situation eventually, but the phrase "no longer support" sounded kind of final.
So, there you are. That's what's been going on with your mail, whether with AOL or probably some other more trendy email service.
OH and I've already cancelled my AOL special service subscription after about 12 hours. So now, I'll be charged nothing. I don't need special tech support for a mail platform that doesn't work for one of my computers running an older OS.