Preventing the drives from spinning down is really a feature which should be controlled by the OS rather than the player.
However, since MC19's release, I have been bugging the JRiver team to change the way that Memory Playback works, so that it would prevent this from ever happening.
In MC19, Memory Playback was changed from caching the files being played, to caching decoded audio, which greatly inflated the amount of memory used, for little-to-no benefit.
I would much rather have seen the additional memory used to cache not only the currently playing file, but the current and next file. This way slow disk/network access would never interfere with playback - the next track to be played is already in memory and loads instantly, and the drive would be spun up at the beginning of a new track to load the next one, allowing minutes for the transfer rather than the last 5-10 seconds at the end of a track which Media Center currently uses.
That said, if you currently have memory playback enabled, you might want to try disabling it.
Rather than loading the track into memory and allowing your drive to spin down, the track will be streamed from the disk which should hopefully keep it active.