I observe similar things with my shared server. It goes away when I complain about it, but comes back a few months later. In my case it is excessive latency on the storage side (systems stays in IOWAIT for ages), at least that is the information that can be gained from within the virtual machine. Access to small things is usually very fast (probably cached in memory), copying large files or doing MD5 checksums on large files takes forever. The throughput may be as low as just a few kb/s.
Causes can be manifold. I assume that storage is handles the NAS way, and these systems are usually quite beefy. Unless the network link (local) is overloaded by too many instances per hardware unit, access should be zippy.
In my case I guess that they move my container onto a machine that has to deal with too many VMs. Usually my system doesn't require a lot of CPU resources, so that would be fine if it weren't for the IO latency when running backups with MD5 sums.
Oh, BTW. I don't use your hoster, but the problem is not limited to them.