Jailbroken? There is a Cydia tweak I use that settled this for me. It's called background manager.
Non JB iOS the best I was able to do was Settings -> General -> Backgroud app refresh -> turn stuff on.
If that helps anyone, hit the Thanks-o-meter thingy, I need to build some street cred to unlock the full forum. LOL.
EDIT: I just noticed in the OP's case that it's a multi-app issue, and tried BM. Currently iOS only allows 1 app at a time to interact with Pebble app. This may be your issue. If you leave more than one companion app running and for example load the watch face for one, then try and go back to the other; you'll find you have to reload that companion app. This irks me as well, but I now a days only use 1 companion app regularly any way. I am unsure of any work around for this on the horizon.