I had that problem as well. My work uses Novell GroupWise, which is accessible via IMAP. Using IMAP I could get my email using the "email" program (not gmail, not work email) just like you. My outgoing emails would get stuck in my outbox if I was using the cell data network, but not if I was on wifi around my office. Every outgoing mail server is configured differently, and clearly my mail server wasn't allowing connections from off-network. My guess is that that's what is going on with you.
There are a few possible solutions:
1) see if your outgoing mail server allows authentication. Often if you authenticate to the outgoing mail server to prove to it that you have a valid mail account, it will send your mail from off-network. This was eventually what I figured out. My outgoing mail server still used port 25, but when I authenticated using TLS, it sent the mail through even off network.
2) try your cell data network's outgoing mail server. If it is Sprint, the outgoing mail server is smtp.sprintpcs.com. It uses port 25, and it accepts authentication. I'm not sure what the login credentials are, though. I know users are given a @sprintpcs.com email address - probably those credentials. If you get this solution to work, your email will still be your work email - the only difference is that your outgoing mail will be routed through sprint's server.