No matter how you copy the project (even with a safe thumb drive, or even with .zip copies), if you store it in an unsafe location it will be at risk. In this case it sounds like it is getting damaged by whatever software (the cloud sync client) is manipulating your disk. It sounds like this cloud service you use, is no good if it’s deleting files behind your back that you just copied into its sync area!
I would stick to using .zip file transfer through this service only, and edit copies of the project outside of its domain. We have some tips and tricks for working that way in a more efficient manner. With the automatic backup feature, it can be very easy (it’s the only way I use sync and I’ve never found it difficult).