In CloudLinux, each user account has its own LVE (Lightweight Virtual Environment).
Each LVE limits the number of processes (Apache processes entering the LVE) to prevent a single site from consuming all Apache processes. If the limit is reached, "mod_hostinglimits" will not be able to continue adding more processes within the LVE and will respond with a code 503 error. In this way, sites that have a lot of resource consumption will gradually slow down as more consumption is having, to the point of seeing the 503 error on the website, without affecting the other users of the server.
Some techniques to reduce server resource consumption can be seen here: https://clientes.atlanticadigital.net/knowledgebase/208 /i-How-to-reduce-CPU-or-Memory-consumption-on-a-website--.html
Or contact us to advise you on the procedure to upgrade your plan to a larger one.