This is a blind shot (haven't tested), but here is my guess: you are creating the same function twice, thus the second replaces the first one. Functions are unique, if you can only have one function as callback of the form submission, you should adapt it to do everything you need within the one function call.
Here's what you could do:
// Sends distinct messages for each recipient
function formSubmitReply(e) {
// First mail recipient and message
MailApp.sendEmail(
e.values[3],
"Help Desk Ticket1",
"Thanks for submitting your issue. \n\nWe'll start " +
"working on it as soon as possible. \n\nHelp Desk",
{name:"Help Desk"}
);
// Second mail recipient and message
MailApp.sendEmail(
e.values[4],
"Help Desk Ticket - FYI form is sent",
"The form a has been submitted. \n\nWe need to start " +
"working on it as soon as possible. \n\nThe Reger Group",
{name:"The Reger Group"}
);
}