If I receive new Apple mail and use my iPhone or iPad to read it first then there is not a problem. However if I open it first on my laptop then the email immediately disappears, but stays on my iphon

SOURCE: Email Support Phone Call 1-(8O5)225-669O Toll Free 24x7 Customer Service Helpline

Setting up incoming pop email from Road Runner to iPhone is straightforward.

Setting up outgoing email is not.

In general, Road Runner requires that you be connected to their network through one of their cable modems in order to use their outgoing SMTP server. Since, an iPhone will never be connected this way, you need to find an alternate way.

There are at least three ways I know of:
1) Send your outgoing mail through Cingular or AT&T's smtp server. This works and is no extra charge, but it has the disadvantage that it only works through the slower EDGE network - not through WIFI.
2) I understand that Google offers free email, and through their free email, you can use their outgoing SMTP servers for your RR account.
3) You can sign up with an outgoing SMTP service like www.authsmtp.com. I use this method. It costs about $25 per year. Your outgoing email works through both EDGE and wifi, and it appears to the recipient as if it came directly from RR.

I recommend either option 2 or 3. The google way is more for a do-it-yourselfer. The authsmtp way is a paid service, so there are good instructions and support. I have several months left with authsmtp, but at some point I may switch to Google. 
I did number 3 and its fantastic!! 

SOURCE: Apple iPhone and Network Solutions web mail

So I had the same problem using a Network Solutions mail account and got it working. Here is what I did:

Name: Whatever you want
Address: [email protected] (user specific) Must include the @domain
Description: same as above
INCOMING MAIL SERVER
User Name: [email protected] (user specific) Must include the @domain
password: password
OUTGOING MAIL SERVER
Host name: smtp.domain.com
Username:no entry
password:no entry

At message that SSL failed select YES to continue without using SSL should get message twice (incoming & outgoing server tests)

Made no changes to Authentication (default-password) or Server port (default-25)

Came up and began to load mail instantly.Sent test mail and all is good.

sandyp4ever

• 19 Answers
• Posted on Mar 13, 2009

SOURCE: using Outlook on my pc - disappearing email on my iPhone

Hi, Possibly this could be the reason. Your iPhone might have been setup with IMAP connection, and Outlook with POP3. In this case, once email is downloaded by Outlook, it will be deleted from the att.net server. So, go to Advanced in your Outlook account configuration and Select the option leave a copy on the server.

Then you will have to delete all the emails individually from your phone too.

Thanks
Sandeep

SOURCE: Yahoo mail. Unable to send email or open attachments

Yahoo Mail has 2 modes: 1.Classic mode and 2.Standard mode I guess you're in standard mode,I suggest you switch to classic mode, I hope it could help you
Good luck

SOURCE: My iphone doesnt countinue opening it just stay in

You need to try to do a hard reset, then a restore. Follow instructions below:
1. Hold down home and power button together until screen turns completely black.
2. Open up iTunes on your computer
3. While holding down the home button, plug your iPhone into your computer and continue holding down home button until iTunes recognizes the iPhone
4. Should see dialog box from iTunes saying, "iTunes has detected an iPhone in Recovery Mode, you must restore this device"
Hope this helps, Please Rate Me!