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We fixed this with offering unlimited disk I/O and unlimited IOPS with a limited NPROC set to around 30-50 according the plan, and never have faced such issues from past 1 year or so. RAM and CPU are limited though, but even with heavy e-commerce websites generating over $2000 a month, play happily with our 4 vCPU and 4GB RAM shared environment. It depends on how well the site is optimized and the database queries.
As said by @cPFence above, Cloudlinux limits are very different as compared to hard limits cgroups by Enhance.