Hotmail: receiving e-mail on my iPhone5

I have a paid Hotmail subscription, which I have used on my iPhone for 3 years with no problem, including while traveling all over the world.  Since September, I have had problems SENDING e-mail from my iPhone whenever I am traveling away from my home-base in CT (where Hotmail continues to work fine on my phone).  I have traveled to NY, Kentucky, and Washington state, and in all 3 locations I have been able to receive my Hotmail on my phone with no problem, but when I tried to send Hotmail from my phone, I frequently received an error message that my "smtp password" was incorrect.  However, the password WAS correct, because the e-mails would sit in my outbox for a couple of hours or for a day, and eventually they would be sent, even while I was still in the same city where I had previously been unable to send mail. The Apple store says it's not an Apple problem; it's a Hotmail problem.  Then, after an hour trying to reach someone by phone, a Microsoft tech support person told me it's probably a problem with my phone provider's roaming service.  BUT, on all occasions, when traveling with my husband, who has the same iPhone that I have and who has the same AT&T mobile account that I have, he could stand right next to me and successfully send e-mail from his phone, while I could not.  When I told this to the Microsoft tech support person, he said there must be something different about the way my husband's phone is set up vs. mine, but Apple refuses to help (they say they do not "support" Hotmail), and the Microsoft tech support guy also refused to help, saying he does not support Hotmail.  He told me to post my problem here.  Help!