This does sound like a RAM issue. Aren't you getting any error messages from Corona? Such as "system is running low on RAM"?
Are you using displacement here?
Are you using multiple render elements? Maybe LightMix?
What you could try is going to devel/debug settings (
https://coronarenderer.freshdesk.com/support/solutions/articles/12000021288) and then checking the "low mem" option. This will probably slow down rendering by about 5%, but will conserve memory.
A workaround which comes to my mind is simply rendering in lower resolution and then enlarging the image in post...
PS. Proxies don't really save RAM in any way, but if you would like to use them, you can convert the Max mesh into proxies, right?