Update: Mantas Kačinskas (a Facebook OW Group user) suggest to change the Stand-By configuration of the OW App.
Yo have to set your Android phone to 'Developer Mode' (check here).
Then you have to go to Developer Settings, System, Advanced Options, Developer Options, scroll a lot until 'StandBy Apps', look for OW App, and ser a higher priority setting: Frequent o Working State.
I've tried and now while the phone is locked, the OW App seems to keep connected.
Anyway. Theses are work arounds, not REAL solutions to the connectivity problems of some BT modules. Since it is a RF problem, is a little bit of hit and miss. Some users have better lucky than others.

@rfkilowatt you're awesome!
Such a detailed post! I twist my ankle windsurfing on Saturday, so the only ones riding my OW XR are my friends. Lots of scratches and lot of envy. The BT connection gets really better with the new Android settings, but is far from perfect.
I will use my rest time to follow your instructions step by step. I don't have a METCAL at home, but I will try to look at the board and find a way of repairing it.
I will update accordingly.
Cheers!

@tlamb2 THIS!
It really works better! I was thinking in opening the board and soldering an external antenna, but this works! I've to test it more time, but great so far!

You've to enter "Developer Mode" in Android.
Go to Settings > System Info (the last on the list), then tap 7 times on the Build Number field (also the last field).
Then go search in settings, and look for AVRCP, then switch to 1.6 as @tlamb2 says.

That's it!

@rfkilowatt @kanguru007 I'm in Argentina so sending to USA is no-way (customs cost as hi as U$S 1000 here).
I'm electronic engineer and I have the right tools, maybe I will try to solder an external antenna (1/4 lambda). What do you think?