I was having delivery issues from this function to Gmail, Yahoo, AOL, etc. I used the notes here to figure that you need to be setting your Return-Path to a valid email to catch bounces. There are two extra delivery gotchas on top of that:
1) The domain in the email used in the -f option in the php.ini sendmail parameter or in the mail() extra parameters field, needs to have a valid SPF record for the domain (in DNS as a "TXT" record type for sure and add an additional "SPF" type record if possible). Why? That's header field being used for spam checks.
2) You should also use a domain key or DKIM. The trick here is that the domain key/DKIM is case sensitive! I used Cpanel to create my domain key which automatically used all lowercase domain names in the key creation. I found when sending email and using a camel case "-f [email protected]" option, my key was not accepted. However it was accepted when I used "-f [email protected]".
There are many other factors that can contribute to mail not getting to inboxes, including your own multiple failed testing attempts, so I suggest you consult each site's guidelines and don't ask me for help. These are just the couple technical issues that helped my case.
I hope this saves someone some time and headaches...