If the Windows 10 Fast Startup feature is enabled, which is the default, when you do a normal Shutdown it will snapshot an image of the current kernel, drivers, and system state in memory to disk and then on boot it'll load from the image but if you do a Restart it doesn't take the snapshot and instead performs a Normal Start where it goes through the normal process of loading the kernel, the drivers and system state component-by-component from the boot drive etc.
So if it's the Restart that makes the pool drive unavailable, that would suggest the issue is occurring during the normal full boot process. I'd try looking in DrivePool's Cog->Troubleshooting->Service Log after a Restart fails to make the drive available, to see if there are any clues there - e.g. it might just be something is timing out the find-and-mount routine, in which case you can increase the CoveFs_WaitFor***Ms entries as described in https://wiki.covecube.com/StableBit_DrivePool_2.x_Advanced_Settings until it picks up.
If you're still stuck after looking at the Log, you can request a support ticket via StableBit's contact form.
EDIT: made it clearer that only the CoveFs_WaitFor***Ms entries (i.e. the ones ending in Ms) are to be changed. The wiki mentions CoveFs_WaitForVolumesOnMount without the Ms, that's a deprecated entry that isn't used by newer versions of DrivePool.