Thanks everyone. Yes, the transmitter is a DX5e, so according to all the Spektrum literature (and the dude in hobby shop) it's supposed to work with that receiver, and most often, it does. Except when it stop communicating mid-flight!
I'll try some of the tricks mentioned and see if reliability goes up. I know I was doing the opposite of some of those tips.
Keep those suggestions coming if you got 'em.