If the teacher had to tune it twice in one day, then it is likely either the strings need to be replaced or there is damage to the fine tuners or the pegs. Of course, it is possible that your DD knock it out of tune or the cello experienced a temperature/humidity change during the day. Either way, you should have the rental company check the instrument and repair as necessary.
Do cellos really stay in tune that well? DD often needs to adjust her violin tuning in the middle of the practice or lesson and so does her teacher.
I can't speak to all cellos; however, the few that I have personally tuned tend to stay in tune (within a reasonable tolerance) unless the temperature/humidity changes too much or you accidentally bump the fine tuners or pegs. In my experience, you do need to tune much more frequently when the strings become very worn, although that is a bigger problem with violins than cellos (you can get away with old strings on a cello more so than on a violin). Although I said tune the cello every day, I actually meant check every day because often you may only need to adjust one or two strings or even none, particularly if the instrument hasn't been moved. Of course, there are a lot of variables. For example, the composition of the strings make a big difference. Again, I can't speak for all cellos much less all string instruments - there may be many musicians who do tune their instruments multiple times during a lesson/practice.
