Emails on IPad, Iphoe and Drod

I have Live Mail on my home computer and also received emails on my I Pad.  In the past two weeks we have added emails to an I Phone 5 and Droid.  We have changed the password on all of these devices to be the same.  Now , all of a sudden we only get sporitiac emails  .They seem to come and go and are not on all of the devices. I have contacted Time Warner, my internet provider, and have not received much help.  They said to contact Microsoft and Microsoft told me that they only support Live Mail online.  Very frustrating. How can we get all of our emails on the home laptop, I pad, I Phone and Droid? Thanks