To put it simply....the bass gets tuned at the start of the rehearsal. Somewhere into the first piece, it has gone at least a half-step flat. Retuned, the pitch goes way low yet again within a few minutes...and repeats that over the next half hour or longer. By the end of rehearsal, it's close to holding its pitch, which makes me think that something is flexing during its down time and gets bent into a stable position over several retunings.
The problem is more than a matter of pitch tweaking. Further, the bass has been to a good local luthier who fit and thinned the uncut bridge that this CCB was delivered with. He also installed the strings.
This problem reminds me of the time I naively bought a set of Red-O-Ray gut strings before a big band New Year's gig and couldn't keep the instrument up to pitch for even one tune.

...except the bass in question has Helicores that tune easily on a healthy bass and hold their pitch once tuned.