Hello Vic, sorry for the delay. We checked and tested many things and nothing seemed compliant for understanding what was going on.
However, the entire flow has been accepted since about 1 week ago, including previously blocked messages, although no one told me to have changed/restarted anything in configurations or network parameters. So it is very strange, but we could stop thinking about this problem for now (and begin working on other ones). The joys of computing...
Thank you again for your support !
Well, here is an update. Following Vic's answer, we were able to make the warnings disappear ("Discarding received non-HL7 data...") although we were already working with MLLP on both sides (sender <--> receiver).
The flow still blocks sometimes though. It occurs with particular messages because abandoning them allows the flow to become running anew (and this flow blocks again when those messages are put back in it). I think that it does not mean that there is no problem in the network anymore, because the receiver is able to process those blocking messages manually. But we could at least put them apart and so not to let the entire flow be blocked.
Maybe could I reply here once more if we find other clues (or even the solution). But at this time we will probably act as I have just described, processing blocking messages manually, and maybe that putting them apart will allow us to find similarities giving us advices for the real solution.
BR 
Thank you Vic, Nigel and Eduard !
It seems that adding "Ens_Util.Log", as suggested, was useful.
Best regards,
Mathieu