This error will report itself to end user as 508 error, "Resource Limit Reached". This happens due to customer hitting entry processes limit. Entry processes limit restricts the number of concurrent connections to dynamic (php & cgi) scripts for the customer. Otherwise, one site could use up all Apache slots, and cause all the sites to go down.

You can diagnose the issue by running:
# lveinfo --period=1d --by-fault=mep --display-username

You can also monitor the user by running:
# lvetop

You can always increase entry processes limit by running:
# lvectl set USER_ID -–maxEntryProcs NEW_LIMIT save

If you also see that user is hitting CPU limit at the same time at the same time as entry processes limit, raising just entry processes limit will not help.User is using too much resources, and you should either increase both, CPU and entry process limits, or user should optimize their script, or user should be upgraded to VPS or something similar.

Be careful adjusting entry processes limit, as it can adversely affect overall system stability.