I have also issues with that and made interesting observations which I described in this thread with an updated summary in the 1st post.https://getmusicbee.com/forum/index.php?topic=23617.0
I have a certain suspicion that there could be a relashionship with the ASIO buffersize to this problem.
If you make only small changes of sample rate, then nothing bad happens, i.e. from 44.1 to 48 kHz or from 88.2 to 96 kHz.
The mess starts when making big jumps, i.e. from 44.1 to 88.2 or higher to put only one example.
What I know is, that the ASIO driver needs to double the ASIO buffersize between 44.1/48 and 88.2/96
and further double when switching up to 176.4/192 kHz as otherwise the buffer is too small.
Could it be the case that the automatic change of ASIO buffersize by the ASIO driver is somehow related to this problem ?
That perhaps the sample rate change by MusicBee needs to "initialize" ASIO in a different way.
A little bit more delay or other parameters ...