I have my Android smartphone with bluetooth on even if it's not connected with the Surface.
To mitigate the problem I have switched off the bluetooth of my smartphone that I typically have very close to the Surface. This seems to be correlated with the issue because yesterday, a full day of work, the Surface bluetooth connection worked nice.
I will continue today, with the same configuration, with the hope to continue to see the connection on.
If everything works as expected I will turn the bluetooth on the smartphone to see if the Surface issue returns back.
I'll keep you posted on the progress.