Andrew
I thank you for your advice regarding being able to exit and restart Locus Map without losing the track recording, which I verified on a dry run. I should have tried that much earlier.
Now, to the disappearance of the offline map:
I set out on my walk today and saw again the lack of map after an hour when I pushed the 'on' button to check my location. There was no network signal at this time. It is fortunate that I have, as an overlay, the public rights of way that I walk and check. I continued to walk for another hour. I noticed at times the 'phone showed 'H' and a reasonable signal. Then it clicked: I touched the 'Maps' tab and discovered my offline map was deselected!
I shall try the newest version of Locus Map when the apparent issues with Android 4.4.4 are resolved and report, accordingly.
One further comment regarding the preservation of track recording: I had forgotten to plug in my power pack when I saw the battery was low. It powered off when I looked next at the screen. I am pleased to report that the track recording was present, still, when, having plugged in the power pack, I could power up the 'phone after a few minutes.