Just a final update to say problem solved. There is/was no problem with OpenSprinkler. Problem was in the long run of underground wire that connected my OpenSprinkler (inside garage) to where the rain sensor was mounted externally (sitting on an outside fence post).
I dismounted the rain sensor from fence post and connected it directly to the OpenSprinkler with a short 6″ wire and tested it and it worked perfectly. I also re-connected long underground wire (formerly connected to external rain sensor) to OpenSprinkler without the sensor on the other end so that it should present “open circuit” to OpenSprinkler, and when I did that I got the toggling on/off status problem. So I reckon there must be some kind of short in the underground wire that was root cause of issue.
I ran a new wire to the external sensor and now all seems to be working properly.
I should have thought to do this check earlier, but in any case, thanks for the support.